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Artykuły w czasopismach na temat „Standard Equilibrium Quantum Systems”

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Data publikacji: 7 września 2023

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1

Venuti, Lorenzo Campos, i Paolo Zanardi. "Theory of temporal fluctuations in isolated quantum systems". International Journal of Modern Physics B 29, nr 14 (22.05.2015): 1530008. http://dx.doi.org/10.1142/s021797921530008x.

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When an isolated quantum system is driven out of equilibrium, expectation values of general observables start oscillating in time. This paper reviews the general theory of such temporal fluctuations. We first survey some results on the strength of such temporal fluctuations. For example temporal fluctuations are exponentially small in the system's volume for generic systems whereas they fall-off algebraically in integrable systems. We then concentrate on the so-called quench scenario where the system is driven out-of-equilibrium under the application of a sudden perturbation. For sufficiently small perturbations, temporal fluctuations of physical observables can be characterized in full generality and can be used as an effective tool to probe quantum criticality of the underlying model. In the off-critical region the distribution becomes Gaussian. Close to criticality the distribution becomes a universal function uniquely characterized by a single critical exponent, that we compute explicitly. This contrasts standard equilibrium quantum fluctuations for which the critical distribution depends on a numerable set of critical coefficients and is known only for limited examples. The possibility of using temporal fluctuations to determine pseudo-critical boundaries in optical lattice experiments is further reviewed.

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2

Álvarez-Estrada, Ramon F. "Approach to Equilibrium of Statistical Systems: Classical Particles and Quantum Fields Off-Equilibrium". Dynamics 3, nr 2 (13.06.2023): 345–78. http://dx.doi.org/10.3390/dynamics3020020.

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Non-equilibrium evolution at absolute temperature T and approach to equilibrium of statistical systems in long-time (t) approximations, using both hierarchies and functional integrals, are reviewed. A classical non-relativistic particle in one spatial dimension, subject to a potential and a heat bath (hb), is described by the non-equilibrium reversible Liouville distribution (W) and equation, with a suitable initial condition. The Boltzmann equilibrium distribution Weq generates orthogonal (Hermite) polynomials Hn in momenta. Suitable moments Wn of W (using the Hn’s) yield a non-equilibrium three-term hierarchy (different from the standard Bogoliubov–Born–Green–Kirkwood–Yvon one), solved through operator continued fractions. After a long-t approximation, the Wn’s yield irreversibly approach to equilibrium. The approach is extended (without hb) to: (i) a non-equilibrium system of N classical non-relativistic particles interacting through repulsive short range potentials and (ii) a classical ϕ4 field theory (without hb). The extension to one non-relativistic quantum particle (with hb) employs the non-equilibrium Wigner function (WQ): difficulties related to non-positivity of WQ are bypassed so as to formulate approximately approach to equilibrium. A non-equilibrium quantum anharmonic oscillator is analyzed differently, through functional integral methods. The latter allows an extension to relativistic quantum ϕ4 field theory (a meson gas off-equilibrium, without hb), facing ultraviolet divergences and renormalization. Genuine simplifications of quantum ϕ4 theory at high T and large distances and long t occur; then, through a new argument for the field-theoretic case, the theory can be approximated by a classical ϕ4 one, yielding an approach to equilibrium.

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3

Žunkovič, Bojan, Alessandro Silva i Michele Fabrizio. "Dynamical phase transitions and Loschmidt echo in the infinite-range XY model". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 374, nr 2069 (13.06.2016): 20150160. http://dx.doi.org/10.1098/rsta.2015.0160.

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We compare two different notions of dynamical phase transitions in closed quantum systems. The first is identified through the time-averaged value of the equilibrium-order parameter, whereas the second corresponds to non-analyticities in the time behaviour of the Loschmidt echo. By exactly solving the dynamics of the infinite-range XY model, we show that in this model non-analyticities of the Loschmidt echo are not connected to standard dynamical phase transitions and are not robust against quantum fluctuations. Furthermore, we show that the existence of either of the two dynamical transitions is not necessarily connected to the equilibrium quantum phase transition.

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4

FEDOROVA, ANTONINA N., i MICHAEL G. ZEITLIN. "PATTERN FORMATION IN QUANTUM ENSEMBLES". International Journal of Modern Physics B 20, nr 11n13 (20.05.2006): 1570–92. http://dx.doi.org/10.1142/s0217979206033875.

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We present a family of methods, analytical and numerical, which can describe behaviour in (non) equilibrium ensembles, both classical and quantum, especially in the complex systems, where the standard approaches cannot be applied. We demonstrate the creation of nontrivial (meta) stable states (patterns), localized, chaotic, entangled or decoherent, from basic localized modes in various collective models arising from the quantum hierarchy of Wigner-von Neumann-Moyal-Lindblad equations, which are the result of "wignerization" procedure of classical BBGKY hierarchy. We present the explicit description of internal quantum dynamics by means of exact analytical/numerical computations.

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5

Chen, Tyler, i Yu-Chen Cheng. "Numerical computation of the equilibrium-reduced density matrix for strongly coupled open quantum systems". Journal of Chemical Physics 157, nr 6 (14.08.2022): 064106. http://dx.doi.org/10.1063/5.0099761.

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We describe a numerical algorithm for approximating the equilibrium-reduced density matrix and the effective (mean force) Hamiltonian for a set of system spins coupled strongly to a set of bath spins when the total system (system + bath) is held in canonical thermal equilibrium by weak coupling with a “super-bath”. Our approach is a generalization of now standard typicality algorithms for computing the quantum expectation value of observables of bare quantum systems via trace estimators and Krylov subspace methods. In particular, our algorithm makes use of the fact that the reduced system density, when the bath is measured in a given random state, tends to concentrate about the corresponding thermodynamic averaged reduced system density. Theoretical error analysis and numerical experiments are given to validate the accuracy of our algorithm. Further numerical experiments demonstrate the potential of our approach for applications including the study of quantum phase transitions and entanglement entropy for long range interaction systems.

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6

Schmidt, Heinz-Jürgen, i Jochen Gemmer. "A Framework for Sequential Measurements and General Jarzynski Equations". Zeitschrift für Naturforschung A 75, nr 3 (26.03.2020): 265–84. http://dx.doi.org/10.1515/zna-2019-0272.

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AbstractWe formulate a statistical model of two sequential measurements and prove a so-called J-equation that leads to various diversifications of the well-known Jarzynski equation including the Crooks dissipation theorem. Moreover, the J-equation entails formulations of the Second Law going back to Wolfgang Pauli. We illustrate this by an analytically solvable example of sequential discrete position–momentum measurements accompanied with the increase of Shannon entropy. The standard form of the J-equation extends the domain of applications of the standard quantum Jarzynski equation in two respects: It includes systems that are initially only in local equilibrium, and it extends this equation to the cases where the local equilibrium is described by microcanononical, canonical, or grand canonical ensembles. Moreover, the case of a periodically driven quantum system in thermal contact with a heat bath is shown to be covered by the theory presented here if the quantum system assumes a quasi-Boltzmann distribution. Finally, we shortly consider the generalised Jarzynski equation in classical statistical mechanics.

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7

Rodríguez, Antonio, Alessandro Pluchino, Ugur Tirnakli, Andrea Rapisarda i Constantino Tsallis. "Nonextensive Footprints in Dissipative and Conservative Dynamical Systems". Symmetry 15, nr 2 (7.02.2023): 444. http://dx.doi.org/10.3390/sym15020444.

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Despite its centennial successes in describing physical systems at thermal equilibrium, Boltzmann–Gibbs (BG) statistical mechanics have exhibited, in the last several decades, several flaws in addressing out-of-equilibrium dynamics of many nonlinear complex systems. In such circumstances, it has been shown that an appropriate generalization of the BG theory, known as nonextensive statistical mechanics and based on nonadditive entropies, is able to satisfactorily handle wide classes of anomalous emerging features and violations of standard equilibrium prescriptions, such as ergodicity, mixing, breakdown of the symmetry of homogeneous occupancy of phase space, and related features. In the present study, we review various important results of nonextensive statistical mechanics for dissipative and conservative dynamical systems. In particular, we discuss applications to both discrete-time systems with a few degrees of freedom and continuous-time ones with many degrees of freedom, as well as to asymptotically scale-free networks and systems with diverse dimensionalities and ranges of interactions, of either classical or quantum nature.

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8

GORDON, GOREN, NOAM EREZ i GERSHON KURIZKI. "ZENO HEATING AND ANTI-ZENO COOLING BY FREQUENT QUANTUM MEASUREMENTS". International Journal of Quantum Information 07, supp01 (styczeń 2009): 49–62. http://dx.doi.org/10.1142/s021974990900475x.

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We study disturbances of thermal equilibrium between two-level systems (TLS) and a bath by frequent and brief quantum measurements of the TLS energy-states. If the measurements induce either the Zeno or the anti-Zeno regime, namely, the slowdown or speedup of the TLS relaxation, then the resulting entropy and temperature of both the system and the bath are found to be completely determined by the measurement rate, and unrelated to what is expected by standard thermodynamical rules that hold for markovian baths. These anomalies allow for very fast control heating, cooling and state-purification (entropy reduction) of quantum systems much sooner than their thermal equilibration time.

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9

Abul-Magd, A. Y. "Superstatistics in Random Matrix Theory". Sultan Qaboos University Journal for Science [SQUJS] 17, nr 2 (1.12.2012): 157. http://dx.doi.org/10.24200/squjs.vol17iss2pp157-169.

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Random matrix theory (RMT) provides a successful model for quantum systems, whose classical counterpart has chaotic dynamics. It is based on two assumptions: (1) matrix-element independence, and (2) base invariance. The last decade witnessed several attempts to extend RMT to describe quantum systems with mixed regular-chaotic dynamics. Most of the proposed generalizations keep the first assumption and violate the second. Recently, several authors have presented other versions of the theory that keep base invariance at the expense of allowing correlations between matrix elements. This is achieved by starting from non-extensive entropies rather than the standard Shannon entropy, or by following the basic prescription of the recently suggested concept of superstatistics. The latter concept was introduced as a generalization of equilibrium thermodynamics to describe non-equilibrium systems by allowing the temperature to fluctuate. We here review the superstatistical generalizations of RMT and illustrate their value by calculating the nearest-neighbor-spacing distributions and comparing the results of calculation with experiments on billiards modeling systems in transition from order to chaos.

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10

Luo, Yu-Chen, i Xiao-Peng Li. "Quantum simulation of interacting fermions". Acta Physica Sinica 71, nr 22 (2022): 226701. http://dx.doi.org/10.7498/aps.71.20221756.

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Fermions are basic building blocks in the standard model. Interactions among these elementary particles determine how they assemble and consequently form various states of matter in our nature. Simulating fermionic degrees of freedom is also a central problem in condensed matter physics and quantum chemistry, which is crucial to understanding high-temperature superconductivity, quantum magnetism and molecular structure and functionality. However, simulating interacting fermions by classical computing generically face the minus sign problem, encountering the exponential computation complexity. Ultracold atoms provide an ideal experimental platform for quantum simulation of interacting fermions. This highly-controllable system enables the realizing of nontrivial fermionic models, by which the physical properties of the models can be obtained by measurements in experiment. This deepens our understanding of related physical mechanisms and help determine the key parameters. In recent years, there have been versatile experimental studies on quantum ground state physics, finite temperature thermal equilibrium, and quantum many-body dynamics, in fermionic quantum simulation systems. Quantum simulation offers an access to the physical problems that are intractable on the classical computer, including studying macroscopic quantum phenomena and microscopic physical mechanisms, which demonstrates the quantum advantages of controllable quantum systems. This paper briefly introduces the model of interacting fermions describing the quantum states of matter in such a system. Then we discuss various states of matter, which can arise in interacting fermionic quantum systems, including Cooper pair superfluids and density-wave orders. These exotic quantum states play important roles in describing high-temperature superconductivity and quantum magnetism, but their simulations on the classical computers have exponentially computational cost. Related researches on quantum simulation of interacting fermions in determining the phase diagrams and equation of states reflect the quantum advantage of such systems.

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11

Bernard, Denis, i Tony Jin. "Solution to the Quantum Symmetric Simple Exclusion Process: The Continuous Case". Communications in Mathematical Physics 384, nr 2 (21.04.2021): 1141–85. http://dx.doi.org/10.1007/s00220-021-04087-x.

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AbstractThe quantum symmetric simple exclusion process (Q-SSEP) is a model for quantum stochastic dynamics of fermions hopping along the edges of a graph with Brownian noisy amplitudes and driven out-of-equilibrium by injection-extraction processes at a few vertices. We present a solution for the invariant probability measure of the one dimensional Q-SSEP in the infinite size limit by constructing the steady correlation functions of the system density matrix and quantum expectation values. These correlation functions code for a rich structure of fluctuating quantum correlations and coherences. Although our construction does not rely on the standard techniques from the theory of integrable systems, it is based on a remarkable interplay between the permutation groups and polynomials. We incidentally point out a possible combinatorial interpretation of the Q-SSEP correlation functions via a surprising connexion with geometric combinatorics and the associahedron polytopes.

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12

Trushechkin, A. S., M. Merkli, J. D. Cresser i J. Anders. "Open quantum system dynamics and the mean force Gibbs state". AVS Quantum Science 4, nr 1 (marzec 2022): 012301. http://dx.doi.org/10.1116/5.0073853.

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The dynamical convergence of a system to the thermal distribution, or Gibbs state, is a standard assumption across all of the physical sciences. The Gibbs state is determined just by temperature and energies of the system. However, at decreasing system sizes, i.e., for nanoscale and quantum systems, the interaction with their environments is not negligible. The question then arises: Is the system's steady state still the Gibbs state? If not, how may the steady state depend on the interaction details? Here, we provide an overview of recent progress on answering these questions. We expand on the state of the art along two general avenues: First, we take the static point-of-view, which postulates the so-called mean force Gibbs state. This view is commonly adopted in the field of strong coupling thermodynamics, where modified laws of thermodynamics and nonequilibrium fluctuation relations are established on the basis of this modified state. Second, we take the dynamical point of view, originating from the field of open quantum systems, which examines the time-asymptotic steady state within two paradigms. We describe the mathematical paradigm, which proves return to equilibrium, i.e., convergence to the mean force Gibbs state, and then discuss a number of microscopic physical methods, particularly master equations. We conclude with a summary of established links between statics and equilibration dynamics and provide an extensive list of open problems. This comprehensive overview will be of interest to researchers in the wider fields of quantum thermodynamics, open quantum systems, mesoscopic physics, statistical physics, and quantum optics and will find applications whenever energy is exchanged on the nanoscale, from quantum chemistry and biology to magnetism and nanoscale heat management.

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13

Carrington, M. E., R. Kobes, G. Kunstatter, D. Pickering i E. Vaz. "Equilibration in an interacting field theory". Canadian Journal of Physics 80, nr 9 (1.09.2002): 987–93. http://dx.doi.org/10.1139/p02-065.

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We use a combination of perturbation theory and numerical techniques to study the equilibration of two interacting fields that are initially at thermal equilibrium at different temperatures. Using standard rules of quantum field theory, we examine the master equations that describe the time evolution of the distribution functions for the two coupled systems. By making a few reasonable assumptions we reduce the resulting coupled integral/differential equations to a pair of differential equations that can be solved numerically relatively easily and which give physically sensible results. PACS No.: 11.10W

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14

Purkayastha, Archak, Giacomo Guarnieri, Steve Campbell, Javier Prior i John Goold. "Periodically refreshed quantum thermal machines". Quantum 6 (8.09.2022): 801. http://dx.doi.org/10.22331/q-2022-09-08-801.

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We introduce unique class of cyclic quantum thermal machines (QTMs) which can maximize their performance at the finite value of cycle duration τ where they are most irreversible. These QTMs are based on single-stroke thermodynamic cycles realized by the non-equilibrium steady state (NESS) of the so-called Periodically Refreshed Baths (PReB) process. We find that such QTMs can interpolate between standard collisional QTMs, which consider repeated interactions with single-site environments, and autonomous QTMs operated by simultaneous coupling to multiple macroscopic baths. We discuss the physical realization of such processes and show that their implementation requires a finite number of copies of the baths. Interestingly, maximizing performance by operating in the most irreversible point as a function of τ comes at the cost of increasing the complexity of realizing such a regime, the latter quantified by the increase in the number of copies of baths required. We demonstrate this physics considering a simple example. We also introduce an elegant description of the PReB process for Gaussian systems in terms of a discrete-time Lyapunov equation. Further, our analysis also reveals interesting connections with Zeno and anti-Zeno effects.

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15

Hangleiter, Dominik, Ingo Roth, Daniel Nagaj i Jens Eisert. "Easing the Monte Carlo sign problem". Science Advances 6, nr 33 (sierpień 2020): eabb8341. http://dx.doi.org/10.1126/sciadv.abb8341.

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Quantum Monte Carlo (QMC) methods are the gold standard for studying equilibrium properties of quantum many-body systems. However, in many interesting situations, QMC methods are faced with a sign problem, causing the severe limitation of an exponential increase in the runtime of the QMC algorithm. In this work, we develop a systematic, generally applicable, and practically feasible methodology for easing the sign problem by efficiently computable basis changes and use it to rigorously assess the sign problem. Our framework introduces measures of non-stoquasticity that—as we demonstrate analytically and numerically—at the same time provide a practically relevant and efficiently computable figure of merit for the severity of the sign problem. Complementing this pragmatic mindset, we prove that easing the sign problem in terms of those measures is generally an NP-complete task for nearest-neighbor Hamiltonians and simple basis choices by a reduction to the MAXCUT-problem.

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16

Campaioli, Francesco, i Jared H. Cole. "Exciton transport in amorphous polymers and the role of morphology and thermalisation". New Journal of Physics 23, nr 11 (1.11.2021): 113038. http://dx.doi.org/10.1088/1367-2630/ac37c7.

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Abstract Understanding the transport mechanism of electronic excitations in conjugated polymers is key to advancing organic optoelectronic applications, such as solar cells, organic light-emitting diodes and flexible electronics. While crystalline polymers can be studied using solid-state techniques based on lattice periodicity, the characterisation of amorphous polymers is hindered by an intermediate regime of disorder and the associated lack of symmetries. To overcome these hurdles we have developed a reduced state quantum master equation approach based on the Merrifield exciton formalism. This new approach allows us to study the dynamics of excitons’ centre of mass and charge separation (CS), going beyond the standard model of charge-neutral Frenkel excitons. Using this model we study exciton transport in conjugated polymers and its dependence on morphology and temperature. Exciton dynamics consists of a thermalisation process, whose features depend on the relative strength of thermal energy, electronic couplings and disorder, resulting in remarkably different transport regimes. By applying this method to representative systems based on poly(p-phenylene vinylene) (PPV) we obtain insight into the role of temperature and disorder on localisation, CS, non-equilibrium dynamics, and experimental accessibility of thermal equilibrium states of excitons in amorphous polymers.

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17

Dubey, Ritesh Kumar, V. J. Menon, M. K. Pandey i D. N. Tripathi. "Entropy Maximization, Cutoff Distribution, and Finite Stellar Masses". Advances in Astronomy 2008 (2008): 1–14. http://dx.doi.org/10.1155/2008/870804.

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Conventional equilibrium statistical mechanics of open gravitational systems is known to be problematical. We first recall that spherical stars/galaxies acquire unbounded radii, become infinitely massive, and evaporate away continuously if one uses the standard Maxwellian distributionfB(which maximizes the usual Boltzmann-Shannon entropy and hence has a tail extending to infinity). Next, we show that these troubles disappear automatically if we employ the exact most probable distributionf(which maximizes the combinatorial entropy and hence possesses a sharp cutoff tail). Finally, if astronomical observation is carried out on a large galaxy, then the Poisson equation together with thermal de Broglie wavelength provides useful information about the cutoff radiusrK, cutoff energyεK, and the huge quantum numberKup to which the cluster exists. Thereby, a refinement over the empirical lowered isothermal King models, is achieved. Numerically, we find that the most probable distribution (MPD) prediction fits well the number density profile near the outer edge of globular clusters.

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18

SHIK, ALEXANDER, HARRY E. RUDA i SLAVA V. ROTKIN. "ELECTROSTATICS OF NANOWIRES AND NANOTUBES: APPLICATION FOR FIELD–EFFECT DEVICES". International Journal of High Speed Electronics and Systems 16, nr 04 (grudzień 2006): 937–58. http://dx.doi.org/10.1142/s0129156406004090.

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We present a quantum and classical theory of electronic devices with one–dimensional (1D) channels made of a single carbon nanotube or a semiconductor nanowire. An essential component of the device theory is a self–consistent model for electrostatics of 1D systems. It is demonstrated that specific screening properties of 1D wires result in a charge distribution in the channel different from that in bulk devices. The drift–diffusion model has been applied for studying transport in a long channel 1D field–effect transistor. A unified self–consistent description is given for both a semiconductor nanowire and a single–wall nanotube. Within this basic model we analytically calculate equilibrium (at zero current) and quasi–equilibrium (at small current) charge distributions in the channel. Numerical results are presented for arbitrary values of the driving current. General analytic expressions, found for basic device characteristic, differ from equations for a standard bulk three–dimensional field–effect device. The device characteristics are shown to be sensitive to the gate and leads geometry and are analyzed separately for bulk, planar and quasi–1D contacts. The basic model is generalized to take into account external charges which can be polarized and/or moving near the channel. These charges change the self–consistent potential profile in the channel and may show up in device properties, for instance, a hysteresis may develop which can have a memory application.

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19

Ischenko, A. A., Y. I. Tarasov i L. Schäfer. "STRUCTURAL DYNAMICS OF FREE MOLECULES AND CONDENSED STATE OF MATTER. Part II. TRANSIENT STRUCTURES IN CHEMICAL REACTIONS". Fine Chemical Technologies 12, nr 4 (28.08.2017): 5–35. http://dx.doi.org/10.32362/2410-6593-2017-12-4-5-35.

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Basic knowledge of mankind so far relates to the description of electrons and atoms in the material in a state of equilibrium, where the behavior changes slowly over time. The electron diffraction with a high temporal and space resolution has opened the possibility of direct observation of the processes occurring in the transient state of the substance (molecular movie). Here it is necessary to provide a temporary resolution of the order of 100 fs, which corresponds to the transition of the system through the energy barrier of the potential surface, which describes the chemical reaction - the process of the breaking and the formation of new bonds between the interacting agents. Thus, the possibility of the investigation of the coherent nuclear dynamics of molecular systems and the condensed matter can be opened. In the past two decades, it has been possible to observe the nuclear motion in the temporal interval corresponding to the period of the nuclear oscillation. The observed coherent changes in the nuclear system at such temporal intervals determine the fundamental shift from the standard kinetics of chemical reactions to the dynamics of the phase trajectory of a single molecule, the molecular quantum state tomography.

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20

Leonardos, Stefanos, i Georgios Piliouras. "Exploration-Exploitation in Multi-Agent Learning: Catastrophe Theory Meets Game Theory". Proceedings of the AAAI Conference on Artificial Intelligence 35, nr 13 (18.05.2021): 11263–71. http://dx.doi.org/10.1609/aaai.v35i13.17343.

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Exploration-exploitation is a powerful and practical tool in multi-agent learning (MAL), however, its effects are far from understood. To make progress in this direction, we study a smooth analogue of Q-learning. We start by showing that our learning model has strong theoretical justification as an optimal model for studying exploration-exploitation. Specifically, we prove that smooth Q-learning has bounded regret in arbitrary games for a cost model that explicitly captures the balance between game and exploration costs and that it always converges to the set of quantal-response equilibria (QRE), the standard solution concept for games under bounded rationality, in weighted potential games with heterogeneous learning agents. In our main task, we then turn to measure the effect of exploration in collective system performance. We characterize the geometry of the QRE surface in low-dimensional MAL systems and link our findings with catastrophe (bifurcation) theory. In particular, as the exploration hyperparameter evolves over-time, the system undergoes phase transitions where the number and stability of equilibria can change radically given an infinitesimal change to the exploration parameter. Based on this, we provide a formal theoretical treatment of how tuning the exploration parameter can provably lead to equilibrium selection with both positive as well as negative (and potentially unbounded) effects to system performance.

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21

ZASPA, Yurii. "HYDRODYNAMIC-WAVE CALIBRATION OF POTENTIALS IN MAXWELLвЂ™S EQUATIONS: NON-LINEAR DYNAMICS AND COHERENCE, COLLAPSE, EXPANSION AND EXCHANGE INTERACTION OF INERTIAL DISSIPATIVE-COLLECTOR DISTURBANCES IN NON-EQUILIBRIUM MEDIA IN THE COMPLEX SPACE. SPIRAL TURBULENCE AND COHERENT STRUCTURES OF THREE-DIMENSIONAL TIME". Herald of Khmelnytskyi National University. Technical sciences 315, nr 6(1) (29.12.2022): 89–97. http://dx.doi.org/10.31891/2307-5732-2022-315-6-89-97.

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The results of the hydrodynamic-wave calibration of the potentials in MaxwellвЂ™s equations and their analogs for the gravitational field, which combine EulerвЂ™s hydrodynamics, MaxwellвЂ™s electrodynamics, and dвЂ™AlembertвЂ™s wave apparatus with quantum principles, are given. The nonlinearity of the equations for the vector-potential with the velocity dimension ensures the interrelationship of different field forms and the cascade transport of energy by the disturbance spectrum. The obtained solutions of these equations for inertial dissipative-collector disturbances, which are characterized by a balance of local and convective acceleration, and also balance local dissipation (accumulation) with local metainertia. The vector-potential (wave function) of such forms includes a complex Euler exponent, the phase of which depends on the coordinates of the disturbances paired in the complex space вЂ“ without distinguishing its real or imaginary half. Reasoned constancy of the phase, which ensures the coherent nature of the propagation of running field forms in complex space, as well as in topologically adequate three-dimensional time. The latter is considered in a cylindrical coordinate system that combines spiral and jet time forms. The correspondence of the components to the Laplace operator (in the spherical spatial coordinate system associated with the pair of disturbances) with respect to the near-acting centrifugal energy of repulsion and the long-range exchange energy of attraction, which collectively provide the mechanisms of collapse, expansion, and dynamic balance of the pair, has been revealed. Coherent resonant forms of motion with a three-dimensional topology of time are highlighted, which are widely represented, in particular, on the spectra of collider resonances, as well as on the spectra of technical, hydrodynamic, geophysical, and space turbulence. It is noted that such turbulence is described precisely by MaxwellвЂ™s equations in the hydrodynamic-wave calibration of potentials, and not by the Navier-Stokes equations, or by the truncated equations of magnetohydrodynamics, which completely ignore the displacement current in MaxwellвЂ™s equations. The obtained calculation results are confirmed by actual data in the systems of different levels of the organization. The main role of inertial dissipative-collector disturbances in the processes of dynamic thermoregulation of the EarthвЂ™s climate during the cyclical change of climatic optimums during ice ages has been established. In this context, criticism of the current noisy concepts of global warming, which exaggerate anthropogenic factors without taking into account the dominant natural factors, is presented. It is indicated that these factors should be considered in an expanded format of complex space and three-dimensional time without artificial constructions and self-limitations inherent, in particular, in modern standard physical models Lambda-CDM and SM.

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22

Rotter, Ingrid. "Equilibrium States in Open Quantum Systems". Entropy 20, nr 6 (6.06.2018): 441. http://dx.doi.org/10.3390/e20060441.

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Kozyrev, S. V., A. A. Mironov, A. E. Teretenkov i I. V. Volovich. "Flows in non-equilibrium quantum systems and quantum photosynthesis". Infinite Dimensional Analysis, Quantum Probability and Related Topics 20, nr 04 (grudzień 2017): 1750021. http://dx.doi.org/10.1142/s0219025717500217.

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A three-level quantum system interacting with non-equilibrium environment is investigated. The stationary state of the system is found (both for non-coherent and coherent environment) and relaxation and decoherence to the stationary state is described. The stationary state of the system will be non-equilibrium and will generate flows. We describe the dependence of the flows on the state of the environment. We also discuss application of this model to the problem of quantum photosynthesis, in particular, to the description of flows of excitons and generation of excitonic coherences.

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24

Calabrese, Pasquale. "Non-equilibrium dynamics of isolated quantum systems". EPJ Web of Conferences 90 (2015): 08001. http://dx.doi.org/10.1051/epjconf/20159008001.

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25

Brüssel, Marc, Eva Perlt, Sebastian B. C. Lehmann, Michael von Domaros i Barbara Kirchner. "Binary systems from quantum cluster equilibrium theory". Journal of Chemical Physics 135, nr 19 (21.11.2011): 194113. http://dx.doi.org/10.1063/1.3662071.

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26

Eisert, J., M. Friesdorf i C. Gogolin. "Quantum many-body systems out of equilibrium". Nature Physics 11, nr 2 (luty 2015): 124–30. http://dx.doi.org/10.1038/nphys3215.

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Monnai, T. "Deviation from equilibrium in macroscopic quantum systems". Physica Scripta T151 (1.11.2012): 014043. http://dx.doi.org/10.1088/0031-8949/2012/t151/014043.

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28

Fannes, M., i A. Verbeure. "Equilibrium conditions for coupled classical-quantum systems". Journal of Physics A: Mathematical and General 20, nr 17 (1.12.1987): 6037–46. http://dx.doi.org/10.1088/0305-4470/20/17/036.

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29

Garrido, Pedro L., Pablo Hurtado, Daniel Manzano i Francisco de los Santos. "Quantum systems in and out of equilibrium". European Physical Journal Special Topics 227, nr 3-4 (wrzesień 2018): 201–2. http://dx.doi.org/10.1140/epjst/e2018-800100-6.

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30

Bedeaux, D., i P. Mazur. "Mesoscopic non-equilibrium thermodynamics for quantum systems". Physica A: Statistical Mechanics and its Applications 298, nr 1-2 (wrzesień 2001): 81–100. http://dx.doi.org/10.1016/s0378-4371(01)00223-0.

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31

Anza, Fabio. "New Equilibrium Ensembles for Isolated Quantum Systems". Entropy 20, nr 10 (29.09.2018): 744. http://dx.doi.org/10.3390/e20100744.

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The unitary dynamics of isolated quantum systems does not allow a pure state to thermalize. Because of that, if an isolated quantum system equilibrates, it will do so to the predictions of the so-called “diagonal ensemble” ρ DE . Building on the intuition provided by Jaynes’ maximum entropy principle, in this paper we present a novel technique to generate progressively better approximations to ρ DE . As an example, we write down a hierarchical set of ensembles which can be used to describe the equilibrium physics of small isolated quantum systems, going beyond the “thermal ansatz” of Gibbs ensembles.

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32

Li, Hong-Rong, Pei Zhang, Hong Gao, Wen-Ting Bi, M. D. Alamri i Fu-Li Li. "Non-Equilibrium Quantum Entanglement in Biological Systems". Chinese Physics Letters 29, nr 4 (kwiecień 2012): 047101. http://dx.doi.org/10.1088/0256-307x/29/4/047101.

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33

Špička, Václav, Peter D. Keefe i Theo M. Nieuwenhuizen. "Non-equilibrium dynamics: quantum systems and foundations of quantum mechanics". European Physical Journal Special Topics 227, nr 15-16 (marzec 2019): 1837–48. http://dx.doi.org/10.1140/epjst/e2019-900018-7.

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34

Reiss, Kevin A., i David K. Campbell. "The Metastable State of Fermi–Pasta–Ulam–Tsingou Models". Entropy 25, nr 2 (6.02.2023): 300. http://dx.doi.org/10.3390/e25020300.

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Classical statistical mechanics has long relied on assumptions such as the equipartition theorem to understand the behavior of the complicated systems of many particles. The successes of this approach are well known, but there are also many well-known issues with classical theories. For some of these, the introduction of quantum mechanics is necessary, e.g., the ultraviolet catastrophe. However, more recently, the validity of assumptions such as the equipartition of energy in classical systems was called into question. For instance, a detailed analysis of a simplified model for blackbody radiation was apparently able to deduce the Stefan–Boltzmann law using purely classical statistical mechanics. This novel approach involved a careful analysis of a “metastable” state which greatly delays the approach to equilibrium. In this paper, we perform a broad analysis of such a metastable state in the classical Fermi–Pasta–Ulam–Tsingou (FPUT) models. We treat both the α-FPUT and β-FPUT models, exploring both quantitative and qualitative behavior. After introducing the models, we validate our methodology by reproducing the well-known FPUT recurrences in both models and confirming earlier results on how the strength of the recurrences depends on a single system parameter. We establish that the metastable state in the FPUT models can be defined by using a single degree-of-freedom measure—the spectral entropy (η)—and show that this measure has the power to quantify the distance from equipartition. For the α-FPUT model, a comparison to the integrable Toda lattice allows us to define rather clearly the lifetime of the metastable state for the standard initial conditions. We next devise a method to measure the lifetime of the metastable state tm in the α-FPUT model that reduces the sensitivity to the exact initial conditions. Our procedure involves averaging over random initial phases in the plane of initial conditions, the P1-Q1 plane. Applying this procedure gives us a power-law scaling for tm, with the important result that the power laws for different system sizes collapse down to the same exponent as Eα2→0. We examine the energy spectrum E(k) over time in the α-FPUT model and again compare the results to those of the Toda model. This analysis tentatively supports a method for an irreversible energy dissipation process suggested by Onorato et al.: four-wave and six-wave resonances as described by the “wave turbulence” theory. We next apply a similar approach to the β-FPUT model. Here, we explore in particular the different behavior for the two different signs of β. Finally, we describe a procedure for calculating tm in the β-FPUT model, a very different task than for the α-FPUT model, because the β-FPUT model is not a truncation of an integrable nonlinear model.

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35

Suzuki, Masuo. "Thermo Field Dynamics in Equilibrium and Non-Equilibrium Interacting Quantum Systems". Journal of the Physical Society of Japan 54, nr 12 (15.12.1985): 4483–85. http://dx.doi.org/10.1143/jpsj.54.4483.

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36

Brunelli, M., A. Xuereb, A. Ferraro, G. De Chiara, N. Kiesel i M. Paternostro. "Out-of-equilibrium thermodynamics of quantum optomechanical systems". New Journal of Physics 17, nr 3 (31.03.2015): 035016. http://dx.doi.org/10.1088/1367-2630/17/3/035016.

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37

Resnick, Andrew. "Interacting systems far from equilibrium: quantum kinetic theory". Contemporary Physics 59, nr 3 (25.05.2018): 318. http://dx.doi.org/10.1080/00107514.2018.1464515.

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38

Mehboudi, Mohammad, Anna Sanpera i Juan M. R. Parrondo. "Fluctuation-dissipation theorem for non-equilibrium quantum systems". Quantum 2 (24.05.2018): 66. http://dx.doi.org/10.22331/q-2018-05-24-66.

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The fluctuation-dissipation theorem (FDT) is a central result in statistical physics, both for classical and quantum systems. It establishes a relationship between the linear response of a system under a time-dependent perturbation and time correlations of certain observables in equilibrium. Here we derive a generalization of the theorem which can be applied to any Markov quantum system and makes use of the symmetric logarithmic derivative (SLD). There are several important benefits from our approach. First, such a formulation clarifies the relation between classical and quantum versions of the equilibrium FDT. Second, and more important, it facilitates the extension of the FDT to arbitrary quantum Markovian evolution, as given by quantum maps. Third, it clarifies the connection between the FDT and quantum metrology in systems with a non-equilibrium steady state.

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39

De Nicola, S., B. Doyon i M. J. Bhaseen. "Stochastic approach to non-equilibrium quantum spin systems". Journal of Physics A: Mathematical and Theoretical 52, nr 5 (10.01.2019): 05LT02. http://dx.doi.org/10.1088/1751-8121/aaf9be.

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40

Rahdar, Z., i B. Lari. "Open quantum systems and thermal non-equilibrium processes". Modern Physics Letters B 34, nr 17 (9.05.2020): 2050194. http://dx.doi.org/10.1142/s0217984920501948.

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In this paper, we investigate the effects of convexity and concavity of states on entanglement of the system under thermal non-equilibrium condition. In this regard, we consider a system consisting of two spin 1/2 particles with Dzyaloshinskii–Moriya (DM) interaction that follows the Tsallis statistics.Also, according to the desired statistics, the effect of environment parameters and the convexity or concavity of the input states on the output behavior of the SWAP gate is obtained.

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41

Stinchcombe, R. B. "Stochastic non-equilibrium systems and quantum spin models". Physica A: Statistical Mechanics and its Applications 224, nr 1-2 (luty 1996): 248–53. http://dx.doi.org/10.1016/0378-4371(95)00316-9.

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42

Riera-Campeny, Andreu, Maria Moreno-Cardoner i Anna Sanpera. "Time crystallinity in open quantum systems". Quantum 4 (25.05.2020): 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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43

Cai, Zi. "Symmetries and effect of time dimension in non-equilibrium quantum matter". Acta Physica Sinica 70, nr 23 (2021): 230310. http://dx.doi.org/10.7498/aps.70.20211741.

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Non-equilibrium quantum many-body systems have attracted considerable attention in the past decades. The scope of the research of this kind of novel system involves interdisciplinary research of condensed matter, atomic and molecular physics, quantum optics, quantum information and quantum computation, as well as the non-equilibrium statistical physics. The non-equilibrium phenomena emerging from the aforementioned quantum systems can exhibit rich and universal behaviors, which have far from being well understood due to the novelties and complexities of these systems, and hence the quantum many-body physics becomes the research highlight. At the same time, with the rapid development of quantum techniques, the understanding of these complex systems is of important practical significance due to their potential applications in quantum computation and quantum manipulation. In this paper, we show our recent progress of non-equilibrium quantum many-body systems. We focus on the novel phenomena closely related to the temporary symmetry breaking, including the exotic quantum matter, quasi-particles as well as the dynamical universality classes in non-equilibrium quantum many-body systems.

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44

Brody, Dorje C., Daniel W. Hook i Lane P. Hughston. "Quantum phase transitions without thermodynamic limits". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, nr 2084 (13.06.2007): 2021–30. http://dx.doi.org/10.1098/rspa.2007.1865.

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A new microcanonical equilibrium state is introduced for quantum systems with finite-dimensional state spaces. Equilibrium is characterized by a uniform distribution on a level surface of the expectation value of the Hamiltonian. The distinguishing feature of the proposed equilibrium state is that the corresponding density of states is a continuous function of the energy, and hence thermodynamic functions are well defined for finite quantum systems. The density of states, however, is not in general an analytic function. It is demonstrated that generic quantum systems therefore exhibit second-order phase transitions at finite temperatures.

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45

Carollo, Angelo, Bernardo Spagnolo i Davide Valenti. "Non-Equilibrium Phenomena in Quantum Systems, Criticality and Metastability". Proceedings 12, nr 1 (29.09.2019): 43. http://dx.doi.org/10.3390/proceedings2019012043.

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We summarise here some relevant results related to non-equilibrium quantum systems. We characterise quantum phase transitions (QPT) in out-of-equilibrium quantum systems through a novel approach based on geometrical and topological properties of mixed quantum systems. We briefly describe results related to non-perturbative studies of the bistable dynamics of a quantum particle coupled to an environment. Finally, we shortly summarise recent studies on the generation of solitons in current-biased long Josephson junctions.

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46

Kallay, Nikola, Tomislav Glušac, Tajana Preočanin i Ana Čop. "Standard states and equilibrium in ionic micellar systems". Colloids and Surfaces A: Physicochemical and Engineering Aspects 347, nr 1-3 (wrzesień 2009): 76–80. http://dx.doi.org/10.1016/j.colsurfa.2008.12.026.

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Dowling, Neil, Pedro Figueroa-Romero, Felix A. Pollock, Philipp Strasberg i Kavan Modi. "Relaxation of Multitime Statistics in Quantum Systems". Quantum 7 (1.06.2023): 1027. http://dx.doi.org/10.22331/q-2023-06-01-1027.

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Equilibrium statistical mechanics provides powerful tools to understand physics at the macroscale. Yet, the question remains how this can be justified based on a microscopic quantum description. Here, we extend the ideas of pure state quantum statistical mechanics, which focus on single time statistics, to show the equilibration of isolated quantum processes. Namely, we show that most multitime observables for sufficiently large times cannot distinguish a nonequilibrium process from an equilibrium one, unless the system is probed for an extremely large number of times or the observable is particularly fine-grained. A corollary of our results is that the size of non-Markovianity and other multitime characteristics of a nonequilibrium process also equilibrate.

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Esfarjani, Keivan, i Yuan Liang. "Equilibrium and Non-Equilibrium Lattice Dynamics of Anharmonic Systems". Entropy 24, nr 11 (1.11.2022): 1585. http://dx.doi.org/10.3390/e24111585.

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In this review, motivated by the recent interest in high-temperature materials, we review our recent progress in theories of lattice dynamics in and out of equilibrium. To investigate thermodynamic properties of anharmonic crystals, the self-consistent phonon theory was developed, mainly in the 1960s, for rare gas atoms and quantum crystals. We have extended this theory to investigate the properties of the equilibrium state of a crystal, including its unit cell shape and size, atomic positions and lattice dynamical properties. Using the equation-of-motion method combined with the fluctuation–dissipation theorem and the Donsker–Furutsu–Novikov (DFN) theorem, this approach was also extended to investigate the non-equilibrium case where there is heat flow across a junction or an interface. The formalism is a classical one and therefore valid at high temperatures.

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Gyftopoulos, Elias P., i Michael R. von Spakovsky. "Quantum-theoretic Shapes of Constituents of Systems in Various States". Journal of Energy Resources Technology 125, nr 1 (1.03.2003): 1–8. http://dx.doi.org/10.1115/1.1525245.

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In previous publications, it has been shown that entropy is a measure of the quantum-theoretic shape of the constituents of a system. In this paper, we present examples of quantum-theoretic shapes of some systems each consisting of one unit of a single constituent, in either a stable (thermodynamic) equilibrium state or in states that are not stable equilibrium. The systems that we consider are a structureless particle confined in either a linear box or a square box, and a harmonic oscillator. In general, we find that the shape of each constituent is “smooth”—without ripples—for each thermodynamic equilibrium state, and oscillatory or rippled for states that are either nonequilibrium or unstable equilibrium.

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Anglés-Castillo, Andreu, Mari Carmen Bañuls, Armando Pérez i Inés De Vega. "Prethermalization of quantum systems interacting with non-equilibrium environments". New Journal of Physics 22, nr 8 (25.08.2020): 083067. http://dx.doi.org/10.1088/1367-2630/aba7f4.

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