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1
Polkovnikov, Anatoli, Krishnendu Sengupta, Alessandro Silva, and Mukund Vengalattore. "Colloquium: Nonequilibrium dynamics of closed interacting quantum systems." Reviews of Modern Physics 83, no. 3 (August 15, 2011): 863–83. http://dx.doi.org/10.1103/revmodphys.83.863.
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Riera-Campeny, Andreu, Maria Moreno-Cardoner, and Anna Sanpera. "Time crystallinity in open quantum systems." Quantum 4 (May 25, 2020): 270. http://dx.doi.org/10.22331/q-2020-05-25-270.
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Time crystals are genuinely non-equilibrium quantum phases of matter that break time-translational symmetry. While in non-equilibrium closed systems time crystals have been experimentally realized, it remains an open question whether or not such a phase survives when systems are coupled to an environment. Although dissipation caused by the coupling to a bath may stabilize time crystals in some regimes, the introduction of incoherent noise may also destroy the time crystalline order. Therefore, the mechanisms that stabilize a time crystal in open and closed systems are not necessarily the same. Here, we propose a way to identify an open system time crystal based on a single object: the Floquet propagator. Armed with such a description we show time-crystalline behavior in an explicitly short-range interacting open system and demonstrate the crucial role of the nature of the decay processes.
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Weidenmüller, Hans A. "Quantum Chaos, Random Matrices, and Irreversibility in Interacting Many-Body Quantum Systems." Entropy 24, no. 7 (July 11, 2022): 959. http://dx.doi.org/10.3390/e24070959.
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The Pauli master equation describes the statistical equilibration of a closed quantum system. Simplifying and generalizing an approach developed in two previous papers, we present a derivation of that equation using concepts developed in quantum chaos and random-matrix theory. We assume that the system consists of subsystems with strong internal mixing. We can then model the system as an ensemble of random matrices. Equilibration results from averaging over the ensemble. The direction of the arrow of time is determined by an (ever-so-small) coupling to the outside world. The master equation holds for sufficiently large times if the average level densities in all subsystems are sufficiently smooth. These conditions are quantified in the text, and leading-order correction terms are given.
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GIAMPAOLO, S. M., F. ILLUMINATI, A. DI LISI, and G. MAZZARELLA. "MASSIVE QUANTUM MEMORIES BY PERIODICALLY INVERTED DYNAMIC EVOLUTIONS." International Journal of Quantum Information 04, no. 03 (June 2006): 507–17. http://dx.doi.org/10.1142/s0219749906001955.
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We introduce a general scheme to realize perfect quantum state reconstruction and storage in systems of interacting qubits. This novel approach is based on the idea of controlling the residual interactions by suitable external controls that, acting on the inter-qubit couplings, yield time-periodic inversions in the dynamical evolution, thus cancelling exactly the effects of quantum state diffusion. We illustrate the method for spin systems on closed rings with XY residual interactions, showing that it enables the massive storage of arbitrarily large numbers of local states, and we demonstrate its robustness against several realistic sources of noise and imperfections.
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Tavanfar, Alireza, Aliasghar Parvizi, and Marco Pezzutto. "Unitary Evolutions Sourced By Interacting Quantum Memories: Closed Quantum Systems Directing Themselves Using Their State Histories." Quantum 7 (May 15, 2023): 1007. http://dx.doi.org/10.22331/q-2023-05-15-1007.
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We propose, formulate and examine novel quantum systems and behavioral phases in which momentary choices of the system's memories interact in order to source the internal interactions and unitary time evolutions of the system. In a closed system of the kind, the unitary evolution operator is updated, moment by moment, by being remade out of the system's `experience', that is, its quantum state history. The `Quantum Memory Made' Hamiltonians (QMM-Hs) which generate these unitary evolutions are Hermitian nonlocal-in-time operators composed of arbitrarily-chosen past-until-present density operators of the closed system or its arbitrary subsystems. The time evolutions of the kind are described by novel nonlocal nonlinear von Neumann and Schrödinger equations. We establish that nontrivial Purely-QMM unitary evolutions are `Robustly Non-Markovian', meaning that the maximum temporal distances between the chosen quantum memories must exceed finite lower bounds which are set by the interaction couplings. After general formulation and considerations, we focus on the sufficiently-involved task of obtaining and classifying behavioral phases of one-qubit pure-state evolutions generated by first-to-third order polynomial QMM-Hs made out of one, two and three quantum memories. The behavioral attractors resulted from QMM-Hs are characterized and classified using QMM two-point-function observables as the natural probes, upon combining analytical methods with extensive numerical analyses. The QMM phase diagrams are shown to be outstandingly rich, having diverse classes of unprecedented unitary evolutions with physically remarkable behaviors. Moreover, we show that QMM interactions cause novel purely-internal dynamical phase transitions. Finally, we suggest independent fundamental and applied domains where the proposed `Experience Centric' Unitary Evolutions can be applied natuarlly and advantageously.
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Andrianov, Alexander A., Mikhail V. Ioffe, Ekaterina A. Izotova, and Oleg O. Novikov. "The Franke–Gorini–Kossakowski–Lindblad–Sudarshan (FGKLS) Equation for Two-Dimensional Systems." Symmetry 14, no. 4 (April 6, 2022): 754. http://dx.doi.org/10.3390/sym14040754.
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Open quantum systems are, in general, described by a density matrix that is evolving under transformations belonging to a dynamical semigroup. They can obey the Franke–Gorini–Kossakowski–Lindblad–Sudarshan (FGKLS) equation. We exhaustively study the case of a Hilbert space of dimension 2. First, we find final fixed states (called pointers) of an evolution of an open system, and we then obtain a general solution to the FGKLS equation and confirm that it converges to a pointer. After this, we check that the solution has physical meaning, i.e., it is Hermitian, positive and has trace equal to 1, and find a moment of time starting from which the FGKLS equation can be used—the range of applicability of the semigroup symmetry. Next, we study the behavior of a solution for a weak interaction with an environment and make a distinction between interacting and non-interacting cases. Finally, we prove that there cannot exist oscillating solutions to the FGKLS equation, which would resemble the behavior of a closed quantum system.
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Maffei, Maria, Patrice A. Camati, and Alexia Auffèves. "Closed-System Solution of the 1D Atom from Collision Model." Entropy 24, no. 2 (January 19, 2022): 151. http://dx.doi.org/10.3390/e24020151.
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Obtaining the total wavefunction evolution of interacting quantum systems provides access to important properties, such as entanglement, shedding light on fundamental aspects, e.g., quantum energetics and thermodynamics, and guiding towards possible application in the fields of quantum computation and communication. We consider a two-level atom (qubit) coupled to the continuum of travelling modes of a field confined in a one-dimensional chiral waveguide. Originally, we treated the light-matter ensemble as a closed, isolated system. We solve its dynamics using a collision model where individual temporal modes of the field locally interact with the qubit in a sequential fashion. This approach allows us to obtain the total wavefunction of the qubit-field system, at any time, when the field starts in a coherent or a single-photon state. Our method is general and can be applied to other initial field states.
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SHARIF, M., and ABDUL JAWAD. "THERMODYNAMICS IN CLOSED UNIVERSE WITH ENTROPY CORRECTIONS." International Journal of Modern Physics D 22, no. 03 (March 2013): 1350014. http://dx.doi.org/10.1142/s0218271813500144.
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We discuss the generalized second law of thermodynamics (GSLT) in three different systems by taking quantum corrections (logarithmic and power law) to cosmological horizon entropy as well as black hole (BH) entropy. First, we consider phantom energy accretion onto the Schwarzschild BH in the closed Friedmann–Robertson–Walker universe and investigate the validity of the GSLT on the apparent and event horizons. In another scenario, we evaluate the critical mass of the Schwarzschild BH with upper and lower bounds under accretion process due to phantom-like modified generalized chaplygin gas. It is found that the GSLT is respected within these bounds and BH cannot accrete outside them. Finally, we explore this law for a closed universe filled with interacting n-components of fluid (in thermal equilibrium case) and with noninteracting dark matter and dark energy components (in thermal nonequilibrium case) on the apparent and event horizons and find conditions for its validity.
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See, Tian Feng. "Few-photon transport in strongly interacting light-matter systems: A scattering approach." International Journal of Quantum Information 17, no. 06 (September 2019): 1950050. http://dx.doi.org/10.1142/s0219749919500503.
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Engineering strong photon–photon interactions at the quantum level have been crucial in various areas of research, notably in quantum information processing and quantum simulation. It is often done by coupling matter strongly to light. A promising way to achieve this is via waveguide quantum electrodynamics (QED). Motivated by these advancements, we study few-photon transport in waveguide QED setups. First, we present a diagrammatic technique to systematically study multiphoton scattering based on the scattering formalism and Green’s function approach. We demonstrate our proposal through physically relevant examples involving scattering of few-photon states from two-level emitters as well as from arrays of correlated Kerr nonlinear resonators described by the Bose–Hubbard model. In the second part, we apply the diagrammatic technique that was developed to perform a comprehensive study on a Bose–Hubbard lattice with a quasi-periodic potential. This model exhibits many-body localisation. We compute the two-photon transmission probability and show that it carries signatures of the underlying localisation transition with close agreement to the participation ratio of the eigenstates. The systematic scattering approach provided in this paper provides a foundation for future works at the interface between quantum optics and condensed matter.
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Shepelin, A. V., A. M. Rostom, V. A. Tomilin, and L. V. Il’ichov. "Multiworld motives by closed time-like curves." Journal of Physics: Conference Series 2081, no. 1 (November 1, 2021): 012029. http://dx.doi.org/10.1088/1742-6596/2081/1/012029.
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Abstract We propose a new model, entitled S-CTC, for description of quantum systems in the presence of CTC – closed time-like curves. The model is based on the viewpoint on any quantum state as an observer’s state of knowledge of the system preparation procedure. We compare and contrast our S-CTC model with D-CTC and P-CTC models and show that S-CTC shares special quantum features with both D-CTC and P-CTC. As far as the interaction of the quantum system with itself coming from the future concerns, S-CTC is formally equivalent to P-CTC. On the other hand, when calculating outcome probabilities for a measurement within the time interval between the entrance and exit of CTC, S-CTC becomes equivalent to D-CTC. Both these models require the concept of alternative realities (worlds) where different measurement outcomes are recorded and alternative connections of these realities by CTC.
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Siyouri, Fatima-Zahra, Hicham Ait Mansour, and Fadoua Elbarrichi. "Studying quantum correlations dynamics in the phase space for continuous-variable Werner states and Bell-diagonal states." International Journal of Geometric Methods in Modern Physics 16, no. 07 (July 2019): 1950109. http://dx.doi.org/10.1142/s0219887819501093.
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We investigate the ability of Wigner function to reveal and measure general quantum correlations in two-qubit open system. For this purpose, we analyze comparatively their dynamics for two different states, continuous-variable Werner states (CWS) and Bell-diagonal states (BDS), independently interacting with dephasing reservoirs. Then, we explore the effects of decreasing the degree of non-Markovianity on their behavior. We show that the presence of both quantum entanglement and quantum discord allow to have a negative Wigner function, in contrast to the result obtained for the closed two-qubit system [F. Siyouri, M. El Baz and Y. Hassouni, The negativity of Wigner function as a measure of quantum correlations, Quantum Inf. Process. 15(10) (2016) 4237–4252]. In fact, we conclude that negativity of Wigner function can be used to capture and quantify the amount of general non-classical correlations in open quantum systems.
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Cong, Shuang, Yuesheng Lou, Jianxiu Liu, and Sen Kuang. "A Convergent Control Strategy for Quantum Systems." Journal of Systems Science and Information 2, no. 3 (June 25, 2014): 255–66. http://dx.doi.org/10.1515/jssi-2014-0255.
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AbstractIn the interaction picture, a sufficient and necessary condition that guarantees the convergence of closed quantum control system is proposed in this paper. Theoretical derivation and the proof show that it is possible to achieve the convergence to the target state by constructing an observable operator in an energy function and selecting control Hamiltonians. Numerical simulation experiments on a four-level system verify the effectiveness of the proposed control strategy.
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Gupta, Arjit Kant, and Anjan K. Gupta. "Acoustic analog to multiple avoided-crossings in two coupled acoustic cavities." American Journal of Physics 90, no. 7 (July 2022): 494–500. http://dx.doi.org/10.1119/5.0067830.
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A closed cylindrical pipe with an inner partition wall forms two one-dimensional cavities. These each exhibit acoustic modes at certain well-defined frequencies. A partial transmission through the partition leads to interactions between the two cavities' modes, and hence to avoided crossings between modes' frequencies. This acoustic system is analogous to a quantum system that has two multi-level interacting sub-systems and, thus, exhibits multiple avoided crossings. Such an acoustic analog is realized and studied by measuring sound transmission as a function of frequency through a pipe with a partially transmitting and movable partition. An excellent agreement is obtained between the experimental results and a simple model based on wave transmission and reflection at different interfaces.
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Žnidarič, Marko, and Marko Ljubotina. "Interaction instability of localization in quasiperiodic systems." Proceedings of the National Academy of Sciences 115, no. 18 (April 16, 2018): 4595–600. http://dx.doi.org/10.1073/pnas.1800589115.
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Integrable models form pillars of theoretical physics because they allow for full analytical understanding. Despite being rare, many realistic systems can be described by models that are close to integrable. Therefore, an important question is how small perturbations influence the behavior of solvable models. This is particularly true for many-body interacting quantum systems where no general theorems about their stability are known. Here, we show that no such theorem can exist by providing an explicit example of a one-dimensional many-body system in a quasiperiodic potential whose transport properties discontinuously change from localization to diffusion upon switching on interaction. This demonstrates an inherent instability of a possible many-body localization in a quasiperiodic potential at small interactions. We also show how the transport properties can be strongly modified by engineering potential at only a few lattice sites.
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Moore, R. A., and T. C. Scott. "A class of physically acceptable, classical, relativistic, many-particle Lagrangians." Canadian Journal of Physics 66, no. 4 (April 1, 1988): 365–68. http://dx.doi.org/10.1139/p88-058.
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It is shown that the Fokker–Wheeler–Feynman theory for relativistic, massive, charged point particles interacting via action-at-a-distance forces of electromagnetic origin can be generalized to define a class of model systems all with the same physically acceptable properties. These properties include the satisfaction of the correct Lorentz covariance, time-reversal symmetry, particle-interchange symmetry, and causality. For closed systems there exists a generalized Hamiltonian function, linear momentum, and angular momentum that are constants of the motion. This generalization thus yields a relativistic, dynamic description of this class, analogous to nonrelativistic classical mechanics. Included in this class, within the appropriate limits, are the so-called linear relativistic scalar and vector interactions. It is anticipated that this work will be useful for the examination and understanding of physical systems, both classically and quantum mechanically, insofar as they can be modelled from a classical approach.
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Ingber, Lester. "Quantum Calcium-Ion Interactions with EEG." Sci 1, no. 1 (December 11, 2018): 7. http://dx.doi.org/10.3390/sci1010007.
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Background: Previous papers have developed a statistical mechanics of neocortical interactions (SMNI) fit to short-term memory and EEG data. Adaptive Simulated Annealing (ASA) has been developed to perform fits to such nonlinear stochastic systems. An N-dimensional path-integral algorithm for quantum systems, qPATHINT, has been developed from classical PATHINT. Both fold short-time propagators (distributions or wave functions) over long times. Previous papers applied qPATHINT to two systems, in neocortical interactions and financial options. Objective: In this paper the quantum path-integral for Calcium ions is used to derive a closed-form analytic solution at arbitrary time that is used to calculate interactions with classical-physics SMNI interactions among scales. Using fits of this SMNI model to EEG data, including these effects, will help determine if this is a reasonable approach. Method: Methods of mathematical-physics for optimization and for path integrals in classical and quantum spaces are used for this project. Studies using supercomputer resources tested various dimensions for their scaling limits. In this paper the quantum path-integral is used to derive a closed-form analytic solution at arbitrary time that is used to calculate interactions with classical-physics SMNI interactions among scales. Results: The mathematical-physics and computer parts of the study are successful, in that there is modest improvement of cost/objective functions used to fit EEG data using these models. Conclusions: This project points to directions for more detailed calculations using more EEG data and qPATHINT at each time slice to propagate quantum calcium waves, synchronized with PATHINT propagation of classical SMNI.
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Ingber, Lester. "Quantum Calcium-Ion Interactions with EEG." Sci 1, no. 1 (December 11, 2018): 7. http://dx.doi.org/10.3390/sci1010007.v1.
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Background: Previous papers have developed a statistical mechanics of neocortical interactions (SMNI) fit to short-term memory and EEG data. Adaptive Simulated Annealing (ASA) has been developed to perform fits to such nonlinear stochastic systems. An N-dimensional path-integral algorithm for quantum systems, qPATHINT, has been developed from classical PATHINT. Both fold short-time propagators (distributions or wave functions) over long times. Previous papers applied qPATHINT to two systems, in neocortical interactions and financial options. Objective: In this paper the quantum path-integral for Calcium ions is used to derive a closed-form analytic solution at arbitrary time that is used to calculate interactions with classical-physics SMNI interactions among scales. Using fits of this SMNI model to EEG data, including these effects, will help determine if this is a reasonable approach. Method: Methods of mathematical-physics for optimization and for path integrals in classical and quantum spaces are used for this project. Studies using supercomputer resources tested various dimensions for their scaling limits. In this paper the quantum path-integral is used to derive a closed-form analytic solution at arbitrary time that is used to calculate interactions with classical-physics SMNI interactions among scales. Results: The mathematical-physics and computer parts of the study are successful, in that there is modest improvement of cost/objective functions used to fit EEG data using these models. Conclusions: This project points to directions for more detailed calculations using more EEG data and qPATHINT at each time slice to propagate quantum calcium waves, synchronized with PATHINT propagation of classical SMNI.
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Ingber, Lester. "Quantum Calcium-Ion Interactions with EEG." Sci 1, no. 1 (March 21, 2019): 20. http://dx.doi.org/10.3390/sci1010020.
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Background: Previous papers have developed a statistical mechanics of neocortical interactions (SMNI) fit to short-term memory and EEG data. Adaptive Simulated Annealing (ASA) has been developed to perform fits to such nonlinear stochastic systems. An N-dimensional path-integral algorithm for quantum systems, qPATHINT, has been developed from classical PATHINT. Both fold short-time propagators (distributions or wave functions) over long times. Previous papers applied qPATHINT to two systems, in neocortical interactions and financial options. Objective: In this paper the quantum path-integral for Calcium ions is used to derive a closed-form analytic solution at arbitrary time that is used to calculate interactions with classical-physics SMNI interactions among scales. Using fits of this SMNI model to EEG data, including these effects, will help determine if this is a reasonable approach. Method: Methods of mathematical-physics for optimization and for path integrals in classical and quantum spaces are used for this project. Studies using supercomputer resources tested various dimensions for their scaling limits. In this paper the quantum path-integral is used to derive a closed-form analytic solution at arbitrary time that is used to calculate interactions with classical-physics SMNI interactions among scales. Results: The mathematical-physics and computer parts of the study are successful, in that there is modest improvement of cost/objective functions used to fit EEG data using these models. Conclusions: This project points to directions for more detailed calculations using more EEG data and qPATHINT at each time slice to propagate quantum calcium waves, synchronized with PATHINT propagation of classical SMNI.
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Brandão, Fernando, Michał Horodecki, Nelly Ng, Jonathan Oppenheim, and Stephanie Wehner. "The second laws of quantum thermodynamics." Proceedings of the National Academy of Sciences 112, no. 11 (February 9, 2015): 3275–79. http://dx.doi.org/10.1073/pnas.1411728112.
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The second law of thermodynamics places constraints on state transformations. It applies to systems composed of many particles, however, we are seeing that one can formulate laws of thermodynamics when only a small number of particles are interacting with a heat bath. Is there a second law of thermodynamics in this regime? Here, we find that for processes which are approximately cyclic, the second law for microscopic systems takes on a different form compared to the macroscopic scale, imposing not just one constraint on state transformations, but an entire family of constraints. We find a family of free energies which generalize the traditional one, and show that they can never increase. The ordinary second law relates to one of these, with the remainder imposing additional constraints on thermodynamic transitions. We find three regimes which determine which family of second laws govern state transitions, depending on how cyclic the process is. In one regime one can cause an apparent violation of the usual second law, through a process of embezzling work from a large system which remains arbitrarily close to its original state. These second laws are relevant for small systems, and also apply to individual macroscopic systems interacting via long-range interactions. By making precise the definition of thermal operations, the laws of thermodynamics are unified in this framework, with the first law defining the class of operations, the zeroth law emerging as an equivalence relation between thermal states, and the remaining laws being monotonicity of our generalized free energies.
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Muschik, Wolfgang. "Concepts of Phenomenological Irreversible Quantum Thermodynamics I: Closed Undecomposed Schottky Systems in Semi-Classical Description." Journal of Non-Equilibrium Thermodynamics 44, no. 1 (January 28, 2019): 1–13. http://dx.doi.org/10.1515/jnet-2018-0087.
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Abstract If the von Neumann equation is modified by time dependent statistical weights, the time rate of entropy, the entropy exchange and the production of a Schottky system are derived whose Hamiltonian does not contain the interaction with the system’s environment. This interaction is semi-classically described by the quantum theoretical expressions of power and entropy exchange.
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Xue, Z., H. Lin, and T. H. Lee. "Analysis and control of closed quantum systems based on real-valued dynamics." IET Control Theory & Applications 6, no. 16 (November 1, 2012): 2576–84. http://dx.doi.org/10.1049/iet-cta.2011.0140.
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HIAI, FUMIO, and DÉNES PETZ. "ENTROPY DENSITIES FOR GIBBS STATES OF QUANTUM SPIN SYSTEMS." Reviews in Mathematical Physics 05, no. 04 (December 1993): 693–712. http://dx.doi.org/10.1142/s0129055x93000218.
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This paper is a contribution to the general theory of quantum spin systems. We deal with a general theory in the sense that no concrete interaction shows up but an arbitrary relatively short-range interaction is chosen. It is well known that the mean entropy plays an important role in the thermodynamics of quantum spin systems: it is one of the ingredients of the Lanford–Ruelle–Robinson variational principle. We show that in the background of the existence of the mean entropy, there is an operator convergence which resembles the McMillan theorem from information theory. Asymptotic equipartition property and several entropy densities are investigated, in particular, the relation of the Gibbs condition to relative entropies. Although this paper is not intended to be a review, we try to give an overview of the theory of quantum Gibbs states in the mathematical sense. The paper is organized as follows. Section 1 provides an introduction and further sections contain our new results. Each section is closed with a short discussion on sources and references.
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ÖZER, OKAN, and BÜLENT GÖNÜL. "NEW EXACT TREATMENT OF THE PERTURBED COULOMB INTERACTIONS." Modern Physics Letters A 18, no. 36 (November 30, 2003): 2581–86. http://dx.doi.org/10.1142/s021773230301199x.
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A novel method for the exact solvability of quantum systems is discussed and used to obtain closed analytical expressions in arbitrary dimensions for the exact solutions of the hydrogenic atom in the external potential ΔV(r) = br + cr2, which is based on the recently introduced supersymmetric perturbation theory.
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Álvarez-Estrada, Ramon. "Non-Equilibrium Liouville and Wigner Equations: Classical Statistical Mechanics and Chemical Reactions for Long Times." Entropy 21, no. 2 (February 14, 2019): 179. http://dx.doi.org/10.3390/e21020179.
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We review and improve previous work on non-equilibrium classical and quantum statistical systems, subject to potentials, without ab initio dissipation. We treat classical closed three-dimensional many-particle interacting systems without any “heat bath” ( h b ), evolving through the Liouville equation for the non-equilibrium classical distribution W c , with initial states describing thermal equilibrium at large distances but non-equilibrium at finite distances. We use Boltzmann’s Gaussian classical equilibrium distribution W c , e q , as weight function to generate orthogonal polynomials ( H n ’s) in momenta. The moments of W c , implied by the H n ’s, fulfill a non-equilibrium hierarchy. Under long-term approximations, the lowest moment dominates the evolution towards thermal equilibrium. A non-increasing Liapunov function characterizes the long-term evolution towards equilibrium. Non-equilibrium chemical reactions involving two and three particles in a h b are studied classically and quantum-mechanically (by using Wigner functions W). Difficulties related to the non-positivity of W are bypassed. Equilibrium Wigner functions W e q generate orthogonal polynomials, which yield non-equilibrium moments of W and hierarchies. In regimes typical of chemical reactions (short thermal wavelength and long times), non-equilibrium hierarchies yield approximate Smoluchowski-like equations displaying dissipation and quantum effects. The study of three-particle chemical reactions is new.
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CSEH, JÓZSEF, JUDIT DARAI, HUITZILIN YEPEZ-MARTINEZ, and PETER O. HESS. "PHASE-TRANSITIONS AND NUCLEAR CLUSTERIZATION." International Journal of Modern Physics E 17, no. 10 (November 2008): 2296–300. http://dx.doi.org/10.1142/s0218301308011501.
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After reviewing some basic features of the temperature-governed phase-transitions in macroscopic systems and in atomic nuclei we consider non-thermal phase-transitions of nuclear structure in the example of cluster states. Phenomenological and semimicroscopical algebraic cluster models with identical interactions are applied to binary cluster systems of closed and non-closed shell clusters. Phase-transitions are observed in each case between the rotational (rigid molecule-like) and vibrational (shell-like) cluster states. The phase of this finite quantum system shows a quasi-dynamical symmetry.
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Dunn, J. Michael, Tobias J. Hagge, Lawrence S. Moss, and Zhenghan Wang. "Quantum logic as motivated by quantum computing." Journal of Symbolic Logic 70, no. 2 (June 2005): 353–59. http://dx.doi.org/10.2178/jsl/1120224716.
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§1. Introduction. Our understanding of Nature comes in layers, so should the development of logic. Classic logic is an indispensable part of our knowledge, and its interactions with computer science have recently dramatically changed our life. A new layer of logic has been developing ever since the discovery of quantum mechanics. G. D. Birkhoff and von Neumann introduced quantum logic in a seminal paper in 1936 [1]. But the definition of quantum logic varies among authors (see [2]). How to capture the logic structure inherent in quantum mechanics is very interesting and challenging. Given the close connection between classical logic and theoretical computer science as exemplified by the coincidence of computable functions through Turing machines, recursive function theory, and λ-calculus, we are interested in how to gain some insights about quantum logic from quantum computing. In this note we make some observations about quantum logic as motivated by quantum computing (see [5]) and hope more people will explore this connection.The quantum logic as envisioned by Birkhoff and von Neumann is based on the lattice of closed subspaces of a Hilbert space, usually an infinite dimensional one. The quantum logic of a fixed Hilbert space ℍ in this note is the variety of all the true equations with finitely many variables using the connectives meet, join and negation. Quantum computing is theoretically based on quantum systems with finite dimensional Hilbert spaces, especially the states space of a qubit ℂ2. (Actually the qubit is merely a convenience.
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González-Gutiérrez, Carlos A., Ricardo Román-Ancheyta, Diego Espitia, and Rosario Lo Franco. "Relations between entanglement and purity in non-Markovian dynamics." International Journal of Quantum Information 14, no. 07 (October 2016): 1650031. http://dx.doi.org/10.1142/s0219749916500313.
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Knowledge of the relationships among different features of quantumness, like entanglement and state purity, is important from both fundamental and practical viewpoints. Yet, this issue remains little explored in dynamical contexts for open quantum systems. We address this problem by studying the dynamics of entanglement and purity for two-qubit systems using paradigmatic models of radiation-matter interaction, with a qubit being isolated from the environment (spectator configuration). We show the effects of the corresponding local quantum channels on an initial two-qubit pure entangled state in the concurrence–purity diagram and find the conditions which enable dynamical closed formulas of concurrence, used to quantify entanglement, as a function of purity. We finally discuss the usefulness of these relations in assessing entanglement and purity thresholds which allow noisy quantum teleportation. Our results provide new insights about how different properties of composite open quantum systems behave and relate each other during quantum evolutions.
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Flambaum, V. V. "Time Dynamics in Chaotic Many-body Systems: Can Chaos Destroy a Quantum Computer?" Australian Journal of Physics 53, no. 4 (2000): 489. http://dx.doi.org/10.1071/ph99091.
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Highly excited many-particle states in quantum systems (nuclei, atoms, quantum dots, spin systems, quantum computers) can be ‘chaotic’ superpositions of mean-field basis states (Slater determinants, products of spin or qubit states). This is a result of the very high energy level density of many-body states which can be easily mixed by a residual interaction between particles. We consider the time dynamics of wave functions and increase of entropy in such chaotic systems. As an example, we present the time evolution in a closed quantum computer. A time scale for the entropy S(t) increase is t c ~τ 0 /(n log 2 n), where τ 0 is the qubit ‘lifetime’, n is the number of qubits, S(0) = 0 and S(t c )=1. At t _ t c the entropy is small: S ~nt 2 J 2 log 2 (1/t 2 J2 ), where J is the inter-qubit interaction strength. At t > t c the number of ‘wrong’ states increases exponentially as 2 S(t) . Therefore, t c may be interpreted as a maximal time for operation of a quantum computer. At t >>t c the system entropy approaches that for chaotic eigenstates.
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Dyszel, Peter, and Jason T. Haraldsen. "Thermodynamics of General Heisenberg Spin Tetramers Composed of Coupled Quantum Dimers." Magnetochemistry 7, no. 2 (February 22, 2021): 29. http://dx.doi.org/10.3390/magnetochemistry7020029.
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Advances in quantum computing technology have been made in recent years due to the evolution of spin clusters. Recent studies have tended towards spin cluster subgeometries to understand more complex structures better. These molecular magnets provide a multitude of phenomena via exchange interactions that allow for advancements in spintronics and other magnetic system applications due to the possibility of increasing speed, data storage, memory, and stability of quantum computing systems. Using the Heisenberg spin–spin exchange Hamiltonian and exact diagonalization, we examine the evolution of quantum energy levels and thermodynamic properties for various spin configurations and exchange interactions. The XXYY quantum spin tetramer considered in this study consists of two coupled dimers with exchange interactions α1J and α1′J and a dimer–dimer exchange interaction α2J. By varying spin values and interaction strengths, we determine the exact energy eigenstates that are used to determine closed-form analytic solutions for the heat capacity and magnetic susceptibility of the system and further analyze the evolution of the properties of the system based on the parameter values chosen. Furthermore, this study shows that the Schottky anomaly shifts towards zero as the ground-state of the system approaches a quantum phase transition between spin states. Additionally, we investigate the development of phase transitions produced by the convergence of the Schottky anomaly with both variable exchange interactions and external magnetic field.
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CLARK, J. W., V. A. KHODEL, and M. V. ZVEREV. "DISSECTING AND TESTING COLLECTIVE AND TOPOLOGICAL SCENARIOS FOR THE QUANTUM CRITICAL POINT." International Journal of Modern Physics B 24, no. 25n26 (October 20, 2010): 4901–14. http://dx.doi.org/10.1142/s0217979210057080.
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In a number of strongly-interacting Fermi systems, the existence of a quantum critical point (QCP) is signaled by a divergent density of states and effective mass at zero temperature. Competing scenarios and corresponding mechanisms for the QCP are contrasted and analyzed. The conventional scenario invokes critical fluctuations of a collective mode in the close vicinity of a second-order phase transition and attributes divergence of the effective mass to a coincident vanishing of the quasiparticle pole strength. It is argued that this collective scenario is disfavored by certain experimental observations as well as theoretical inconsistencies, including violation of conservation laws applicable in the strongly interacting medium. An alternative topological scenario for the QCP is developed self-consistently within the general framework of Landau quasiparticle theory. In this scenario, the topology of the Fermi surface is transfigured when the quasiparticle group velocity vanishes at the QCP, yet the quasiparticle picture remains meaningful and no symmetry is broken. The topological scenario is found to explain the non-Fermi-liquid behavior observed experimentally in Yb-based heavy-fermion systems close to the QCP. This study suggests that integration of the topological scenario with the theory of second-order, symmetry-breaking quantum phase transitions will furnish a proper foundation for theoretical understanding of the extended QCP region.
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Hu, Qing, Dafei Jin, Jun Xiao, Sang Hoon Nam, Xiaoze Liu, Yongmin Liu, Xiang Zhang, and Nicholas X. Fang. "Ultrafast fluorescent decay induced by metal-mediated dipole–dipole interaction in two-dimensional molecular aggregates." Proceedings of the National Academy of Sciences 114, no. 38 (September 5, 2017): 10017–22. http://dx.doi.org/10.1073/pnas.1703000114.
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Two-dimensional molecular aggregate (2DMA), a thin sheet of strongly interacting dipole molecules self-assembled at close distance on an ordered lattice, is a fascinating fluorescent material. It is distinctively different from the conventional (single or colloidal) dye molecules and quantum dots. In this paper, we verify that when a 2DMA is placed at a nanometric distance from a metallic substrate, the strong and coherent interaction between the dipoles inside the 2DMA dominates its fluorescent decay at a picosecond timescale. Our streak-camera lifetime measurement and interacting lattice–dipole calculation reveal that the metal-mediated dipole–dipole interaction shortens the fluorescent lifetime to about one-half and increases the energy dissipation rate by 10 times that expected from the noninteracting single-dipole picture. Our finding can enrich our understanding of nanoscale energy transfer in molecular excitonic systems and may designate a unique direction for developing fast and efficient optoelectronic devices.
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Kapustin, Anton, and Nikita Sopenko. "Local Noether theorem for quantum lattice systems and topological invariants of gapped states." Journal of Mathematical Physics 63, no. 9 (September 1, 2022): 091903. http://dx.doi.org/10.1063/5.0085964.
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We study generalizations of the Berry phase for quantum lattice systems in arbitrary dimensions. For a smooth family of gapped ground states in d dimensions, we define a closed d + 2-form on the parameter space, which generalizes the curvature of the Berry connection. Its cohomology class is a topological invariant of the family. When the family is equivariant under the action of a compact Lie group G, topological invariants take values in the equivariant cohomology of the parameter space. These invariants unify and generalize the Hall conductance and the Thouless pump. A key role in these constructions is played by a certain differential graded Fréchet–Lie algebra attached to any quantum lattice system. As a by-product, we describe ambiguities in charge densities and conserved currents for arbitrary lattice systems with rapidly decaying interactions.
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Leaw, Jia Ning, Ho-Kin Tang, Maxim Trushin, Fakher F. Assaad, and Shaffique Adam. "Universal Fermi-surface anisotropy renormalization for interacting Dirac fermions with long-range interactions." Proceedings of the National Academy of Sciences 116, no. 52 (December 9, 2019): 26431–34. http://dx.doi.org/10.1073/pnas.1913096116.
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Recent experimental [I. Joet al.,Phys. Rev. Lett.119, 016402 (2017)] and numerical [M. Ippoliti, S. D. Geraedts, R. N. Bhatt,Phys. Rev. B95, 201104 (2017)] evidence suggests an intriguing universal relationship between the Fermi surface anisotropy of the noninteracting parent 2-dimensional (2D) electron gas and the strongly correlated composite Fermi liquid formed in a strong magnetic field close to half-filling. Inspired by these observations, we explore more generally the question of anisotropy renormalization in interacting 2D Fermi systems. Using a recently developed [H. -K. Tanget al.,Science361, 570 (2018)] nonperturbative and numerically exact projective quantum Monte Carlo simulation as well as other numerical and analytic techniques, only for Dirac fermions with long-range Coulomb interactions do we find a universal square-root decrease of the Fermi-surface anisotropy. For theν=1/2composite Fermi liquid, this result is surprising since a Dirac fermion ground state was only recently proposed as an alternative to the usual Halperin–Lee–Read state. Our proposed universality can be tested in several anisotropic Dirac materials including graphene, topological insulators, organic conductors, and magic-angle twisted bilayer graphene.
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Nietner, A., B. Vanhecke, F. Verstraete, J. Eisert, and L. Vanderstraeten. "Efficient variational contraction of two-dimensional tensor networks with a non-trivial unit cell." Quantum 4 (September 21, 2020): 328. http://dx.doi.org/10.22331/q-2020-09-21-328.
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Tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems in classical statistical mechanics. While tensor networks can now be seen as becoming standard tools in the description of such complex many-body systems, close to optimal variational principles based on such states are less obvious to come by. In this work, we generalize a recently proposed variational uniform matrix product state algorithm for capturing one-dimensional quantum lattices in the thermodynamic limit, to the study of regular two-dimensional tensor networks with a non-trivial unit cell. A key property of the algorithm is a computational effort that scales linearly rather than exponentially in the size of the unit cell. We demonstrate the performance of our approach on the computation of the classical partition functions of the antiferromagnetic Ising model and interacting dimers on the square lattice, as well as of a quantum doped resonating valence bond state.
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Yu, Xinlei, Tong Jin, Kun Wang, Dan Li, and Longjiu Cheng. "Benchmark studies on the large errors of calculated binding energies in metallophilic interactions." Journal of Chemical Physics 156, no. 10 (March 14, 2022): 104103. http://dx.doi.org/10.1063/5.0085213.
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Aurophilicity is a d10–d10 closed-shell interaction, which is repulsively calculated by the Hartree–Fork (HF) method, whereas binding energies ( Eb) are largely overestimated under the second-order Møller–Plesset (MP2) method, compared to the coupled cluster singles and doubles with perturbative triples [CCSD(T)] method. The unusual energy errors between different wave functional methods were also verified in other closed-shell metallophilic systems and even were taken as a label of metallophilic interaction. Here, we performed a benchmark study on a collection of structures with weak interactions, sp–sp bonds, sp–d bonds, and d–d bonds, to investigate the influence factor of the errors of HF and MP2 methods. It was found that the large energy errors of HF and MP2 methods were not specified for closed-shell interactions, and the errors could also be very large for many covalent bonds, which was strongly related to the azimuthal quantum number of interaction orbitals. Compared to the CCSD(T) method, the MP2 method weakens the s–s covalent interactions slightly, strengthens the p–p covalent interactions slightly, and overestimates the d–d covalent interactions largely (can be −170 kcal/mol for the Re–Re quadruple bond). This benchmark study suggests that the special energy errors in metallophilicity may result from the participation of d orbitals. Benchmark studies on various density functional methods were also given for calculating binding energies of d–d bonds.
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Башмакова, Е. Н., Е. А. Вашукевич, and Т. Ю. Голубева. "Параллельная многокубитная эволюция в протоколе квантового неразрушающего взаимодействия." Оптика и спектроскопия 131, no. 7 (2023): 949. http://dx.doi.org/10.21883/os.2023.07.56130.4902-23.
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To date, two-qubit quantum logic gates have become an essential part of quantum computing. The study of methods for their implementation is an important practical problem for various quantum optical and information applications. In this paper, we have considered a protocol for multimode quantum non demolition interaction between an atomic ensemble and multimode light with orbital angular momentum in order to analyze the applicability of this protocol in discrete variables computing. We have developed a multimode interaction Hamiltonian and analyzed the dynamics of field and atomic variables depending on the structure of the driving field. We discuss in detail the procedure for separating qubit noninteracting subsystems on a set of atomic and field modes for various values of the orbital angular momentum of the driving field. Such a procedure helps to reduce the considered protocol to the parallel evolution of two-qubit closed systems.
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Poznanski, Roman, Eda Alemdar, Cacha Lleuvelyn, Valeriy Sbitnev, and Erkki Brandas. "Journal of Multiscale Neuroscience." Journal of Multiscale Neuroscience 1, no. 2 (October 28, 2022): 109–33. http://dx.doi.org/10.56280/1546792195.
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information based on an inter-cerebral superfast, spontaneous information pathway involving protein-protein interactions. Protons are convenient quantum objects for transferring bit units in a complex water medium like the brain. The phonon-polariton interaction in such a medium adds informational complexity involving complex protein interactions that are essential for the superfluid-like highway to enable the consciousness process to penetrate brain regions due to different regulated gene sets as opposed to single region-specific genes. Protein pathways in the cerebral cortices are connected in a single network of thousands of proteins. To understand the role of inter-cerebral communication, we postulate protonic currents in interfacial water crystal lattices result from phonon-polariton vibrations, which can lead in the presence of an electromagnetic field, to ultra-rapid communication where thermo-qubits, physical feelings, and protons that are convenient quantum objects for transferring bit units in a complex water medium. The relative equality between the frequencies of thermal oscillations due to the energy of the quasi-protonic movement about a closed loop and the frequencies of electromagnetic oscillations confirms the existence of quasi-polaritons. Phonon-polaritons are electromagnetic waves coupled to lattice vibrational modes. Still, when generated specifically by protons, they are referred to as phonon-coupled quasi-particles, i.e., providing a coupling with vibrational motions. We start from quasiparticles and move up the scale to biomolecular communication in subcellular, cellular and neuronal structures, leading to the negentropic entanglement of multiscale ‘bits’ of information. Espousing quantum potential chemistry, the interdependence of intrinsic information on the negative gain in the steady-state represents the mesoscopic aggregate of the microscopic random quantum-thermal fluctuations expressed through a negentropically derived, temperature-dependent, dissipative quantum potential energy. The latter depends on the time derivative of the spread function and temperature, which fundamentally explains the holonomic brain theory.
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Molčanov, Krešimir, and Biserka Kojić-Prodić. "Towards understanding π-stacking interactions between non-aromatic rings." IUCrJ 6, no. 2 (February 2, 2019): 156–66. http://dx.doi.org/10.1107/s2052252519000186.
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The first systematic study of π interactions between non-aromatic rings, based on the authors' own results from an experimental X-ray charge-density analysis assisted by quantum chemical calculations, is presented. The landmark (non-aromatic) examples include quinoid rings, planar radicals and metal-chelate rings. The results can be summarized as: (i) non-aromatic planar polyenic rings can be stacked, (ii) interactions are more pronounced between systems or rings with little or no π-electron delocalization (e.g. quinones) than those involving delocalized systems (e.g. aromatics), and (iii) the main component of the interaction is electrostatic/multipolar between closed-shell rings, whereas (iv) interactions between radicals involve a significant covalent contribution (multicentric bonding). Thus, stacking covers a wide range of interactions and energies, ranging from weak dispersion to unlocalized two-electron multicentric covalent bonding (`pancake bonding'), allowing a face-to-face stacking arrangement in some chemical species (quinone anions). The predominant interaction in a particular stacked system modulates the physical properties and defines a strategy for crystal engineering of functional materials.
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Braak, Daniel. "Symmetries in the Quantum Rabi Model." Symmetry 11, no. 10 (October 9, 2019): 1259. http://dx.doi.org/10.3390/sym11101259.
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The quantum Rabi model is the simplest and most important theoretical description of light–matter interaction for all experimentally accessible coupling regimes. It can be solved exactly and is even integrable due to a discrete symmetry, the Z 2 or parity symmetry. All qualitative properties of its spectrum, especially the differences to the Jaynes–Cummings model, which possesses a larger, continuous symmetry, can be understood in terms of the so-called “G-functions” whose zeroes yield the exact eigenvalues of the Rabi Hamiltonian. The special type of integrability appearing in systems with discrete degrees of freedom is responsible for the absence of Poissonian level statistics in the spectrum while its well-known “Juddian” solutions are a natural consequence of the structure of the G-functions. The poles of these functions are known in closed form, which allows drawing conclusions about the global spectrum.
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Frassek, Rouven, and Cristian Giardinà. "Exact solution of an integrable non-equilibrium particle system." Journal of Mathematical Physics 63, no. 10 (October 1, 2022): 103301. http://dx.doi.org/10.1063/5.0086715.
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We consider the integrable family of symmetric boundary-driven interacting particle systems that arise from the non-compact XXX Heisenberg model in one dimension with open boundaries. In contrast to the well-known symmetric exclusion process, the number of particles at each site is unbounded. We show that a finite chain of N sites connected at its ends to two reservoirs can be solved exactly, i.e., the factorial moments of the non-equilibrium steady-state can be written in the closed form for each N. The solution relies on probabilistic arguments and techniques inspired by integrable systems. It is obtained in two steps: (i) the introduction of a dual absorbing process reducing the problem to a finite number of particles and (ii) the solution of the dual dynamics exploiting a symmetry obtained from the quantum inverse scattering method. Long-range correlations are computed in the finite-volume system. The exact solution allows us to prove by a direct computation that, in the thermodynamic limit, the system approaches local equilibrium. A by-product of the solution is the algebraic construction of a direct mapping between the non-equilibrium steady state and the equilibrium reversible measure.
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Gelbwaser-Klimovsky, D., N. Erez, R. Alicki, and G. Kurizki. "Can quantum control modify thermodynamic behavior?" Canadian Journal of Chemistry 92, no. 2 (February 2014): 160–67. http://dx.doi.org/10.1139/cjc-2013-0327.
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We review the effects of frequent, impulsive quantum nondemolition measurements of the energy of two-level systems, alias qubits, in contact with a thermal bath. The resulting entropy and temperature of the system subject to measurements at intervals below the bath memory (Markovianity) time are completely determined by the measurement rate. Namely, they are unrelated to what is expected by standard thermodynamical behavior that holds for Markovian baths. These anomalies allow for very fast control of heating, cooling, and state-purification (entropy reduction) of qubits, much sooner than their thermal equilibration time. We further show that frequent measurements may enable the extraction of work in a closed cycle from the system−bath interaction (correlation) energy, a hitherto unexploited work resource. They allow for work even if no information is gathered or the bath is at zero temperature, provided the cycle is within the bath memory time.
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Gulden, Tobias, and Alex Kamenev. "Dynamics of Ion Channels via Non-Hermitian Quantum Mechanics." Entropy 23, no. 1 (January 19, 2021): 125. http://dx.doi.org/10.3390/e23010125.
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We study dynamics and thermodynamics of ion transport in narrow, water-filled channels, considered as effective 1D Coulomb systems. The long range nature of the inter-ion interactions comes about due to the dielectric constants mismatch between the water and the surrounding medium, confining the electric filed to stay mostly within the water-filled channel. Statistical mechanics of such Coulomb systems is dominated by entropic effects which may be accurately accounted for by mapping onto an effective quantum mechanics. In presence of multivalent ions the corresponding quantum mechanics appears to be non-Hermitian. In this review we discuss a framework for semiclassical calculations for the effective non-Hermitian Hamiltonians. Non-Hermiticity elevates WKB action integrals from the real line to closed cycles on a complex Riemann surfaces where direct calculations are not attainable. We circumvent this issue by applying tools from algebraic topology, such as the Picard-Fuchs equation. We discuss how its solutions relate to the thermodynamics and correlation functions of multivalent solutions within narrow, water-filled channels.
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Pagano, Guido, Aniruddha Bapat, Patrick Becker, Katherine S. Collins, Arinjoy De, Paul W. Hess, Harvey B. Kaplan, et al. "Quantum approximate optimization of the long-range Ising model with a trapped-ion quantum simulator." Proceedings of the National Academy of Sciences 117, no. 41 (October 6, 2020): 25396–401. http://dx.doi.org/10.1073/pnas.2006373117.
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Quantum computers and simulators may offer significant advantages over their classical counterparts, providing insights into quantum many-body systems and possibly improving performance for solving exponentially hard problems, such as optimization and satisfiability. Here, we report the implementation of a low-depth Quantum Approximate Optimization Algorithm (QAOA) using an analog quantum simulator. We estimate the ground-state energy of the Transverse Field Ising Model with long-range interactions with tunable range, and we optimize the corresponding combinatorial classical problem by sampling the QAOA output with high-fidelity, single-shot, individual qubit measurements. We execute the algorithm with both an exhaustive search and closed-loop optimization of the variational parameters, approximating the ground-state energy with up to 40 trapped-ion qubits. We benchmark the experiment with bootstrapping heuristic methods scaling polynomially with the system size. We observe, in agreement with numerics, that the QAOA performance does not degrade significantly as we scale up the system size and that the runtime is approximately independent from the number of qubits. We finally give a comprehensive analysis of the errors occurring in our system, a crucial step in the path forward toward the application of the QAOA to more general problem instances.
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Kellar, Samuel, Ka-Ming Tam, and Juana Moreno. "Non-Fermi Liquid Behavior in the Three-Dimensional Hubbard Model." Crystals 13, no. 1 (January 6, 2023): 106. http://dx.doi.org/10.3390/cryst13010106.
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We present a numerical study on the non-Fermi liquid behavior of a three-dimensional strongly correlated system. The Hubbard model in a simple cubic lattice is simulated by the dynamical cluster approximation; in particular, the quasi-particle weight is calculated at finite dopings for a range of temperatures. By fitting the quasi-particle weight to the marginal Fermi liquid form at finite doping near the putative quantum critical point, we find evidence of a separatrix between Fermi liquid and non-Fermi liquid regions. Our results suggest that a marginal Fermi liquid and possibly a quantum critical point exist in the non-symmetry broken solution of the three-dimensional interacting electron systems. We also calculate the spectral function, close to the half-filling, and we obtain evidence of pseudogap.
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NAÓN, CARLOS M., MARIANO J. SALVAY, and MARTA L. TROBO. "FUNCTIONAL BOSONIZATION WITH TIME DEPENDENT PERTURBATIONS." International Journal of Modern Physics A 19, no. 29 (November 20, 2004): 4953–71. http://dx.doi.org/10.1142/s0217751x04020695.
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We extend a path-integral approach to bosonization previously developed in the framework of equilibrium Quantum Field Theories, to the case in which time-dependent interactions are taken into account. In particular we consider a noncovariant version of the Thirring model in the presence of a dynamic barrier at zero temperature. By using the Closed Time Path (Schwinger–Keldysh) formalism, we compute the Green's function and the Total Energy Density of the system. Since our model contains the Tomonaga–Luttinger model as a particular case, we make contact with recent results on nonequilibrium electronic systems.
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Varadwaj, Pradeep R. "Tetrel Bonding in Anion Recognition: A First Principles Investigation." Molecules 27, no. 23 (December 2, 2022): 8449. http://dx.doi.org/10.3390/molecules27238449.
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Twenty-five molecule–anion complex systems [I4Tt···X−] (Tt = C, Si, Ge, Sn and Pb; X = F, Cl, Br, I and At) were examined using density functional theory (ωB97X-D) and ab initio (MP2 and CCSD) methods to demonstrate the ability of the tetrel atoms in molecular entities, I4Tt, to recognize the halide anions when in close proximity. The tetrel bond strength for the [I4C···X−] series and [I4Tt···X−] (Tt = Si, Sn; X = I, At), was weak-to-moderate, whereas that in the remaining 16 complexes was dative tetrel bond type with very large interaction energies and short Tt···X close contact distances. The basis set superposition error corrected interaction energies calculated with the highest-level theory applied, [CCSD(T)/def2-TZVPPD], ranged from −3.0 to −112.2 kcal mol−1. The significant variation in interaction energies was realized as a result of different levels of tetrel bonding environment between the interacting partners at the equilibrium geometries of the complex systems. Although the ωB97X-D computed intermolecular geometries and interaction energies of a majority of the [I4Tt···X−] complexes were close to those predicted by the highest level of theory, the MP2 results were shown to be misleading for some of these systems. To provide insight into the nature of the intermolecular chemical bonding environment in the 25 molecule–anion complexes investigated, we discussed the charge-density-based topological and isosurface features that emanated from the application of the quantum theory of atoms in molecules and independent gradient model approaches, respectively.
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Pandey, Sarvesh Kumar, Mohammad Faheem Khan, Shikha Awasthi, Reetu Sangwan, and Sudha Jain. "A Quantum Theory of Atoms-in-Molecules Perspective and DFT Study of Two Natural Products: Trans-Communic Acid and Imbricatolic Acid." Australian Journal of Chemistry 70, no. 3 (2017): 328. http://dx.doi.org/10.1071/ch16406.
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The topological features of the charge densities, ρ(r), and the chemical reactivity of two most biologically relevant and chemically interesting scaffold systems i.e. trans-communic acid and imbricatolic acid have been determined using density functional theory. To identify, characterize, and quantify efficiently, the non-covalent interactions of the atoms in the molecules have been investigated quantitatively using Bader's quantum theory of atoms-in-molecules (QTAIM) technique. The bond path is shown to persist for a range of weak H···H as well as C···H internuclear distances (in the range of 2.0–3.0 Å). These interactions exhibit all the hallmarks of a closed-shell weak interaction. To get insights into both systems, chemical reactivity descriptors, such as HOMO–LUMO, ionization potential, and chemical hardness, have been calculated and used to probe the relative stability and chemical reactivity. Some other useful information is also obtained with the help of several other electronic parameters, which are closely related to the chemical reactivity and reaction paths of the products investigated. Trans-communic acid seems to be chemically more sensitive when compared with imbricatolic acid due to its experimentally observed higher half-maximal inhibitory concentration (bioactivity parameter) value, which is in accordance with its higher chemical reactivity as theoretically predicted using density functional theory-based reactivity index. The quantum chemical calculations have also been performed in solution using different solvents, and the relative order of their structural and electronic properties as well as QTAIM-based parameters show patterns similar to those observed in gas phase only. This study further exemplifies the use and successful application of the bond path concept and the quantum theory of atoms-in-molecules.
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Belousov, Yury, Igor Chernousov, and Vladimir Man’ko. "Pseudo-Qutrit Formed by Two Interacting Identical Spins (s = 1/2) in a Variable External Magnetic Field." Entropy 25, no. 5 (April 26, 2023): 716. http://dx.doi.org/10.3390/e25050716.
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An analytical solution is obtained for the problem of two interacting, identical but separated spin 1/2 particles in a time-dependent external magnetic field, in a general case. The solution involves isolating the pseudo-qutrit subsystem from a two-qubit system. It is shown that the quantum dynamics of a pseudo-qutrit system with a magnetic dipole–dipole interaction can be described clearly and accurately in an adiabatic representation, using a time-dependent basis set. The transition probabilities between the energy levels for an adiabatically varying magnetic field, which follows the Landau–Majorana–Stuckelberg–Zener (LMSZ) model within a short time interval, are illustrated in the appropriate graphs. It is shown that for close energy levels and entangled states, the transition probabilities are not small and strongly depend on the time. These results provide insight into the degree of entanglement of two spins (qubits) over time. Furthermore, the results are applicable to more complex systems with a time-dependent Hamiltonian.
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ACCARDI, LUIGI. "NOISE AND DISSIPATION IN QUANTUM THEORY." Reviews in Mathematical Physics 02, no. 02 (January 1990): 127–76. http://dx.doi.org/10.1142/s0129055x90000065.
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A model independent generalization of quantum mechanics, including the usual as well as the dissipative quantum systems, is proposed. The theory is developed deductively from the basic principles of the standard quantum theory, the only new qualitative assumption being that we allow the wave operator at time t of a quantum system to be non-differentiable (in t) in the usual sense, but only in an appropriately defined (Sec. 5) stochastic sense. The resulting theory is shown to lead to a natural generalization of the usual quantum equations of motion, both in the form of the Schrödinger equation in interaction representation (Sec. 6) and of the Heisenberg equation (Sec. 8). The former equation leads in particular to a quantum fluctuation-dissipation relation of Einstein’s type. The latter equation is a generalized Langevin equation, from which the known form of the generalized master equation can be deduced via the quantum Feynmann-Kac technique (Secs. 9 and 10). For quantum noises with increments commuting with the past the quantum Langevin equation defines a closed system of (usually nonlinear) stochastic differential equations for the observables defining the coefficients of the noises. Such systems are parametrized by certain Lie algebras of observables of the system (Sec. 10). With appropriate choices of these Lie algebras one can deduce generalizations and corrections of several phenomenological equations previously introduced at different times to explain different phenomena. Two examples are considered: the Lie algebra [q, p]=i (Sec. 12), which is shown to lead to the equations of the damped harmonic oscillator; and the Lie algebra of SO(3) (Sec. 13) which is shown to lead to the Bloch equations. In both cases the equations obtained are independent of the model of noise. Moreover, in the former case, it is proved that the only possible noises which preserve the commutation relations of p, q are the quantum Brownian motions, commonly used in laser theory and solid state physics.
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Tung. "CO-EXISTENCE OF LOCALIZED MAGNETIC MOMENT AND DELOCALIZED ELECTRONIC SHELL IN SUB-NANOMETER KONDO-LIKE SYSTEMS." Journal of Military Science and Technology, no. 68 (August 3, 2020): 143–49. http://dx.doi.org/10.54939/1859-1043.j.mst.68.2020.143-149.
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Looking for the smallest limit that the Kondo-like effect can be observed has been a long-standing interest in the field of fundamental physics. In this regard, we have investigated the interaction between a countable number of free electrons and a single impurity magnetic moment in two typical quantum systems Cu12Cr and Au19Cr clusters. Both icosahedral Cu12Cr and tetrahedral Au19Cr clusters tend to form a closed-shell electron structure. However, their magnetic moments are completely different. Using density functional theory calculations, we analyzed, discussed and proposed a co-existence picture of electronic and magnetic shell to explain the quenched and unquenched magnetic moment of Cu12Cr and Au19Cr. The finding results are expected to contribute to the understanding of molecular magnetism in bimetallic nanoclusters.