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1
Rahmani, Faramarz, and Mehdi Golshani. "Some clarifications about the Bohmian geodesic deviation equation and Raychaudhuri’s equation." International Journal of Modern Physics A 33, no. 03 (January 30, 2018): 1850027. http://dx.doi.org/10.1142/s0217751x18500276.
Повний текст джерелаАнотація:
One of the important and famous topics in general theory of relativity and gravitation is the problem of geodesic deviation and its related singularity theorems. An interesting subject is the investigation of these concepts when quantum effects are considered. Since the definition of trajectory is not possible in the framework of standard quantum mechanics (SQM), we investigate the problem of geodesic equation and its related topics in the framework of Bohmian quantum mechanics in which the definition of trajectory is possible. We do this in a fixed background and we do not consider the backreaction effects of matter on the space–time metric.
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Mandal, Bikramaditya, Alexander Semenov, and Dmitri Babikov. "Adiabatic Trajectory Approximation within the Framework of Mixed Quantum/Classical Theory." Journal of Physical Chemistry A 124, no. 47 (November 16, 2020): 9877–88. http://dx.doi.org/10.1021/acs.jpca.0c07547.
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Garashchuk, Sophya. "Description of Bound Reactive Dynamics within the Approximate Quantum Trajectory Framework†." Journal of Physical Chemistry A 113, no. 16 (April 23, 2009): 4451–56. http://dx.doi.org/10.1021/jp8110869.
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Liu, Cheng-Zhou, and Qiao-Jun Cao. "Particle tunneling in a quantum corrected spacetime." Modern Physics Letters A 30, no. 02 (January 15, 2015): 1550007. http://dx.doi.org/10.1142/s0217732315500078.
Повний текст джерелаАнотація:
Particle tunneling from a quantum corrected black hole in the gravity's rainbow was investigated by the radial trajectory method of the tunneling framework. Using the thermodynamic property of the event horizon, a simpler method for calculating the tunneling probability was shown. In this method, the Painleve coordinate transformation of spacetime and the radial trajectory equation of the tunneling particles used in the previous radial trajectory method was not used. Using the simpler method, the tunneling probability of outgoing particles, regardless of whether they are massless or massive, were calculated in a unified way. The emission rates were related to the changes of the black hole entropies before and after the emission. This implies that the emission spectrum agrees with the underling unitary theory. In addition, the Bekenstein–Hawking area for the modified black hole was established and the emission spectrum with quantum corrections was discussed.
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BARCHIELLI, A., M. GREGORATTI, and M. LICCIARDO. "QUANTUM TRAJECTORIES, FEEDBACK AND SQUEEZING." International Journal of Quantum Information 06, supp01 (July 2008): 581–87. http://dx.doi.org/10.1142/s0219749908003815.
Повний текст джерелаАнотація:
Quantum trajectory theory is the best mathematical set up to model continual observations of a quantum system and feedback based on the observed output. Inside this framework, we study how to enhance the squeezing of the fluorescence light emitted by a two-level atom, stimulated by a coherent monochromatic laser. In the presence of a Wiseman-Milburn feedback scheme, based on the homodyne detection of a fraction of the emitted light, we analyze the squeezing dependence on the various control parameters.
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Beyer, Konstantin, Kimmo Luoma, Tim Lenz, and Walter T. Strunz. "Measured Composite Collision Models: Quantum Trajectory Purities and Channel Divisibility." Entropy 24, no. 5 (May 17, 2022): 715. http://dx.doi.org/10.3390/e24050715.
Повний текст джерелаАнотація:
We investigate a composite quantum collision model with measurements on the memory part, which effectively probe the system. The framework allows us to adjust the measurement strength, thereby tuning the dynamical map of the system. For a two-qubit setup with a symmetric and informationally complete measurement on the memory, we study the divisibility of the resulting dynamics in dependence of the measurement strength. The measurements give rise to quantum trajectories of the system and we show that the average asymptotic purity depends on the specific form of the measurement. With the help of numerical simulations, we demonstrate that the different performance of the measurements is generic and holds for almost all interaction gates between the system and the memory in the composite collision model. The discrete model is then extended to a time-continuous limit.
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Burnett, Christopher L., Darryl D. Holm, and David M. Meier. "Inexact trajectory planning and inverse problems in the Hamilton–Pontryagin framework." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2160 (December 8, 2013): 20130249. http://dx.doi.org/10.1098/rspa.2013.0249.
Повний текст джерелаАнотація:
We study a trajectory-planning problem whose solution path evolves by means of a Lie group action and passes near a designated set of target positions at particular times. This is a higher-order variational problem in optimal control, motivated by potential applications in computational anatomy and quantum control. Reduction by symmetry in such problems naturally summons methods from Lie group theory and Riemannian geometry. A geometrically illuminating form of the Euler–Lagrange equations is obtained from a higher-order Hamilton–Pontryagin variational formulation. In this context, the previously known node equations are recovered with a new interpretation as Legendre–Ostrogradsky momenta possessing certain conservation properties. Three example applications are discussed as well as a numerical integration scheme that follows naturally from the Hamilton–Pontryagin principle and preserves the geometric properties of the continuous-time solution.
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Peter, Patrick. "Using Trajectories in Quantum Cosmology." Universe 4, no. 8 (August 15, 2018): 89. http://dx.doi.org/10.3390/universe4080089.
Повний текст джерелаАнотація:
Quantum cosmology based on the Wheeler De Witt equation represents a simple way to implement plausible quantum effects in a gravitational setup. In its minisuperspace version wherein one restricts attention to FLRW metrics with a single scale factor and only a few degrees of freedom describing matter, one can obtain exact solutions and thus acquire full knowledge of the wave function. Although this is the usual way to treat a quantum mechanical system, it turns out however to be essentially meaningless in a cosmological framework. Turning to a trajectory approach then provides an effective means of deriving physical consequences.
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Chiribella, Giulio, and Hlér Kristjánsson. "Quantum Shannon theory with superpositions of trajectories." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2225 (May 2019): 20180903. http://dx.doi.org/10.1098/rspa.2018.0903.
Повний текст джерелаАнотація:
Shannon's theory of information was built on the assumption that the information carriers were classical systems. Its quantum counterpart, quantum Shannon theory, explores the new possibilities arising when the information carriers are quantum systems. Traditionally, quantum Shannon theory has focused on scenarios where the internal state of the information carriers is quantum, while their trajectory is classical. Here we propose a second level of quantization where both the information and its propagation in space–time is treated quantum mechanically. The framework is illustrated with a number of examples, showcasing some of the counterintuitive phenomena taking place when information travels simultaneously through multiple transmission lines.
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Alipour, Sahar, Aurelia Chenu, Ali T. Rezakhani, and Adolfo del Campo. "Shortcuts to Adiabaticity in Driven Open Quantum Systems: Balanced Gain and Loss and Non-Markovian Evolution." Quantum 4 (September 28, 2020): 336. http://dx.doi.org/10.22331/q-2020-09-28-336.
Повний текст джерелаАнотація:
A universal scheme is introduced to speed up the dynamics of a driven open quantum system along a prescribed trajectory of interest. This framework generalizes counterdiabatic driving to open quantum processes. Shortcuts to adiabaticity designed in this fashion can be implemented in two alternative physical scenarios: one characterized by the presence of balanced gain and loss, the other involves non-Markovian dynamics with time-dependent Lindblad operators. As an illustration, we engineer superadiabatic cooling, heating, and isothermal strokes for a two-level system, and provide a protocol for the fast thermalization of a quantum oscillator.
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Yang, Ciann-Dong, and Shiang-Yi Han. "Extending Quantum Probability from Real Axis to Complex Plane." Entropy 23, no. 2 (February 8, 2021): 210. http://dx.doi.org/10.3390/e23020210.
Повний текст джерелаАнотація:
Probability is an important question in the ontological interpretation of quantum mechanics. It has been discussed in some trajectory interpretations such as Bohmian mechanics and stochastic mechanics. New questions arise when the probability domain extends to the complex space, including the generation of complex trajectory, the definition of the complex probability, and the relation of the complex probability to the quantum probability. The complex treatment proposed in this article applies the optimal quantum guidance law to derive the stochastic differential equation governing a particle’s random motion in the complex plane. The probability distribution ρc(t,x,y) of the particle’s position over the complex plane z=x+iy is formed by an ensemble of the complex quantum random trajectories, which are solved from the complex stochastic differential equation. Meanwhile, the probability distribution ρc(t,x,y) is verified by the solution of the complex Fokker–Planck equation. It is shown that quantum probability |Ψ|2 and classical probability can be integrated under the framework of complex probability ρc(t,x,y), such that they can both be derived from ρc(t,x,y) by different statistical ways of collecting spatial points.
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VARMA, RAM K. "Some surprising manifestations of charged particle dynamics in a magnetic field." Journal of Plasma Physics 76, no. 3-4 (January 15, 2010): 355–67. http://dx.doi.org/10.1017/s0022377809990626.
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AbstractWe present here some very unusual experimental results on the dynamics of charged particle in a magnetic field which cannot be comprehended in terms of the Lorentz dynamics regarded, as per the current conceptual framework, as the appropriate one for the macro-scale description. Astonishingly, these results have been shown to be manifestations of a novel macro-scale quantum structure, designated as ‘transition amplitude wave’ (TAW), riding with the guiding centre trajectory, which is generated in the latter trajectory in consequence of the scattering of the particle with a fixed scattering centre. One set of observed results is thus identified as matter wave interference effects on the macro-scale attributable to this entity. The other enigmatic observation demonstrates the detection of a curl-free magnetic vector potential on the macro-scale, which is also shown to be a consequence of the TAW embedded in the Lorentz trajectory. These enigmatic results thus point to the unravelling of a new concept of a ‘dressed’ Lorentz trajectory—dressed with the TAW—accountable for these results, as against the ‘bare’ trajectory. These results and the formalism which enables one to comprehend them have led to the emergence of a new class of phenomena which display quantum properties on the macro-scale.
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Strasberg, Philipp. "Thermodynamics of Quantum Causal Models: An Inclusive, Hamiltonian Approach." Quantum 4 (March 2, 2020): 240. http://dx.doi.org/10.22331/q-2020-03-02-240.
Повний текст джерелаАнотація:
Operational quantum stochastic thermodynamics is a recently proposed theory to study the thermodynamics of open systems based on the rigorous notion of a quantum stochastic process or quantum causal model. In there, a stochastic trajectory is defined solely in terms of experimentally accessible measurement results, which serve as the basis to define the corresponding thermodynamic quantities. In contrast to this observer-dependent point of view, a `black box', which evolves unitarily and can simulate a quantum causal model, is constructed here. The quantum thermodynamics of this big isolated system can then be studied using widely accepted arguments from statistical mechanics. It is shown that the resulting definitions of internal energy, heat, work, and entropy have a natural extension to the trajectory level. The canonical choice of them coincides with the proclaimed definitions of operational quantum stochastic thermodynamics, thereby providing strong support in favour of that novel framework. However, a few remaining ambiguities in the definition of stochastic work and heat are also discovered and in light of these findings some other proposals are reconsidered. Finally, it is demonstrated that the first and second law hold for an even wider range of scenarios than previously thought, covering a large class of quantum causal models based solely on a single assumption about the initial system-bath state.
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Yang, Ciann-Dong, and Shiang-Yi Han. "Tunneling Quantum Dynamics in Ammonia." International Journal of Molecular Sciences 22, no. 15 (July 31, 2021): 8282. http://dx.doi.org/10.3390/ijms22158282.
Повний текст джерелаАнотація:
Ammonia is a well-known example of a two-state system and must be described in quantum-mechanical terms. In this article, we will explain the tunneling phenomenon that occurs in ammonia molecules from the perspective of trajectory-based quantum dynamics, rather than the usual quantum probability perspective. The tunneling of the nitrogen atom through the potential barrier in ammonia is not merely a probability problem; there are underlying reasons and mechanisms explaining why and how the tunneling in ammonia can happen. Under the framework of quantum Hamilton mechanics, the tunneling motion of the nitrogen atom in ammonia can be described deterministically in terms of the quantum trajectories of the nitrogen atom and the quantum forces applied. The vibrations of the nitrogen atom about its two equilibrium positions are analyzed in terms of its quantum trajectories, which are solved from the Hamilton equations of motion. The vibration periods are then computed by the quantum trajectories and compared with the experimental measurements.
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Brizuela, David, and Tomasz Pawłowski. "Quantum fluctuations and semiclassicality in an inflaton-driven evolution." Journal of Cosmology and Astroparticle Physics 2022, no. 10 (October 1, 2022): 080. http://dx.doi.org/10.1088/1475-7516/2022/10/080.
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Abstract A semiclassical description of quantum systems is applied to probe the dynamics of the cosmological model of an inflationary universe with quadratic inflaton potential, described in a quantum framework of geometrodynamics. The systematic analysis, focusing in particular on the inflationary and post-inflationary epochs, revealed several surprising and counterintuitive features: (i) during inflation the universe rapidly spreads out in volume which leads to significant relative variance by the end of inflation; (ii) despite that, the quantum evolution can still be described to high accuracy by semiclassical methods; (iii) moreover, in the post-inflationary epoch, as the order of included quantum corrections increases, the quantum trajectory approaches the classical one and the description involving second-order corrections only is actually the least accurate there. The consequence of the latter is that the effects of the quantum variances are washed out by the higher-order quantum corrections.
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Tessarotto, Massimo, and Claudio Cremaschini. "Role of Quantum Entropy and Establishment of H-Theorems in the Presence of Graviton Sinks for Manifestly-Covariant Quantum Gravity." Entropy 21, no. 4 (April 19, 2019): 418. http://dx.doi.org/10.3390/e21040418.
Повний текст джерелаАнотація:
Based on the introduction of a suitable quantum functional, identified here with the Boltzmann–Shannon entropy, entropic properties of the quantum gravitational field are investigated in the framework of manifestly-covariant quantum gravity theory. In particular, focus is given to gravitational quantum states in a background de Sitter space-time, with the addition of possible quantum non-unitarity effects modeled in terms of an effective quantum graviton sink localized near the de Sitter event horizon. The theory of manifestly-covariant quantum gravity developed accordingly is shown to retain its emergent-gravity features, which are recovered when the generalized-Lagrangian-path formalism is adopted, yielding a stochastic trajectory-based representation of the quantum wave equation. This permits the analytic determination of the quantum probability density function associated with the quantum gravity state, represented in terms of a generally dynamically-evolving shifted Gaussian function. As an application, the study of the entropic properties of quantum gravity is developed and the conditions for the existence of a local H-theorem or, alternatively, of a constant H-theorem are established.
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Huang, Jung-Jeng. "Bohm Quantum Trajectories of Scalar Field in Trans-Planckian Physics." Advances in High Energy Physics 2012 (2012): 1–19. http://dx.doi.org/10.1155/2012/312841.
Повний текст джерелаАнотація:
In lattice Schrödinger picture, we investigate the possible effects of trans-Planckian physics on the quantum trajectories of scalar field in de Sitter space within the framework of the pilot-wave theory of de Broglie and Bohm. For the massless minimally coupled scalar field and the Corley-Jacobson type dispersion relation with sextic correction to the standard-squared linear relation, we obtain the time evolution of vacuum state of the scalar field during slow-roll inflation. We find that there exists a transition in the evolution of the quantum trajectory from well before horizon exit to well after horizon exit, which provides a possible mechanism to solve the riddle of the smallness of the cosmological constant.
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IHM, JISOON. "BROKEN TIME-REVERSAL SYMMETRY AND BERRY’S PHASE." International Journal of Modern Physics B 07, no. 11 (May 15, 1993): 2109–46. http://dx.doi.org/10.1142/s0217979293002808.
Повний текст джерелаАнотація:
Berry’s phase is typically realized in a system consisting of fast and slow variables, when the trajectory of the slow variable makes a closed loop. The quantum mechanical phase picked up by the fast variable while the slow variable traverses the loop has turned out to produce real physical effects through quantum interference. In this article, we investigate origins of Berry’s geometric phase and show that they are in general attributable to the broken time-reversal symmetry of the system. Our analysis leads to the classification of Berry’s phase for Hamiltonian systems in terms of symmetry properties under time-reversal operations. Spontaneous time-reversal symmetry-breaking of state vectors is shown to give rise to Berry’s phase as exemplified by a quantum-mechanical rotated hoop. A system with an explicitly time-reversal symmetry-breaking Hamiltonian is also demonstrated to exhibit nontrivial Berry’s phase. The quantization of the geometric phase associated with the real two-dimensional Hamiltonian having topological singularity is explained within the same framework. The unique role of the time-reversal operator among general antiunitary operators is also discussed.
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Villaseco Arribas, Evaristo, Federica Agostini, and Neepa T. Maitra. "Exact Factorization Adventures: A Promising Approach for Non-Bound States." Molecules 27, no. 13 (June 22, 2022): 4002. http://dx.doi.org/10.3390/molecules27134002.
Повний текст джерелаАнотація:
Modeling the dynamics of non-bound states in molecules requires an accurate description of how electronic motion affects nuclear motion and vice-versa. The exact factorization (XF) approach offers a unique perspective, in that it provides potentials that act on the nuclear subsystem or electronic subsystem, which contain the effects of the coupling to the other subsystem in an exact way. We briefly review the various applications of the XF idea in different realms, and how features of these potentials aid in the interpretation of two different laser-driven dissociation mechanisms. We present a detailed study of the different ways the coupling terms in recently-developed XF-based mixed quantum-classical approximations are evaluated, where either truly coupled trajectories, or auxiliary trajectories that mimic the coupling are used, and discuss their effect in both a surface-hopping framework as well as the rigorously-derived coupled-trajectory mixed quantum-classical approach.
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Hucul, D., M. Yeo, W. K. Hensinger, J. Rabchuk, S. Olmschenk, and C. Monroe. "On the transport of atomic ions in linear and multidimensional ion trap arrays." Quantum Information and Computation 8, no. 6&7 (July 2008): 501–78. http://dx.doi.org/10.26421/qic8.6-7-1.
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Trapped atomic ions have become one of the most promising architectures for a quantum computer, and current effort is now devoted to the transport of trapped ions through complex segmented ion trap structures in order to scale up to much larger numbers of trapped ion qubits. This paper covers several important issues relevant to ion transport in any type of complex multidimensional rf (Paul) ion trap array. We develop a general theoretical framework for the application of time-dependent electric fields to shuttle laser-cooled ions along any desired trajectory, and describe a method for determining the effect of arbitrary shuttling schedules on the quantum state of trapped ion motion. In addition to the general case of linear shuttling over short distances, we introduce issues particular to the shuttling through multidimensional junctions, which are required for the arbitrary control of the positions of large arrays of trapped ions. This includes the transport of ions around a corner, through a cross or T junction, and the swapping of positions of multiple ions in a laser-cooled crystal. Where possible, we make connections to recent experimental results in a multidimensional T junction trap, where arbitrary 2-dimensional transport was realized.
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Sukker, Ghader M., Nuha Wazzan, Ashour Ahmed, and Rifaat Hilal. "Conformation and electronic structure of Carbidopa. A QM/MD study." Journal of Theoretical and Computational Chemistry 15, no. 01 (February 2016): 1650002. http://dx.doi.org/10.1142/s0219633616500024.
Повний текст джерелаАнотація:
Carbidopa (CD) is a drug used in combination with L-dopa (LD) in treatment of Parkinson’s disease (PD). CD is an inhibitor for enzyme decarboxylase, yet its mode of action is not entirely known although it is believed to involve enzyme shape recognition. The present work attempts to investigate the conformational preferences of CD. Tight geometry optimization at the density functional theory (DFT)/B3LYP/6-311[Formula: see text]G** level of theory has been carried out. The shallow nature of the potential energy surface (PES) and the presence of several local minima within a small energy range necessitate the launching of DFT-based molecular dynamics (MD) simulations. Two MD experiments were submitted for 35,000 points each. The complete trajectory in time domain of 10.5 ps is analyzed and discussed. The global minimum energy structure of CD is localized and identified by subsequent frequency calculations. The quantum theory of atom in molecules (QTAIMs) is used to extract and compare the quantum chemical topology features of the electron density distribution in CD and LD. Bonding characteristics are analyzed and discussed within the natural bond orbital (NBO) framework.
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Yu, Wenjing, Zi Li, Yuting Peng, Xinxin Feng, Tianlv Xu, Herbert Früchtl, Tanja van Mourik, Steven R. Kirk, and Samantha Jenkins. "Controlling Achiral and Chiral Properties with an Electric Field: A Next-Generation QTAIM Interpretation." Symmetry 14, no. 10 (October 6, 2022): 2075. http://dx.doi.org/10.3390/sym14102075.
Повний текст джерелаАнотація:
We used the recently introduced stress tensor trajectory Uσ space construction within the framework of next-generation quantum theory of atoms in molecules (NG-QTAIM) for a chirality investigation of alanine when subjected to a non-structurally distorting electric field. The resultant sliding of the axial-bond critical point (BCP) responded significantly, up to twice as much, in the presence of the applied electric field in comparison to its absence. The bond flexing, a measure of bond strain, was always lower by up to a factor of four in the presence of the electric field, depending on its direction and magnitude. An achiral character of up to 7% was found for alanine in the presence of the applied electric field. The achiral character was entirely absent in the presence of the lowest value of the applied electric field. Future applications, including molecular devices using left and right circularly polarized laser pulses, are briefly discussed.
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Alamro, Hayam, Hamed Alqahtani, Fahad F. Alruwaili, Sumayh S. Aljameel, and Mohammed Rizwanullah. "Blockchain with Quantum Mayfly Optimization-Based Clustering Scheme for Secure and Smart Transport Systems." Sustainability 15, no. 15 (July 31, 2023): 11782. http://dx.doi.org/10.3390/su151511782.
Повний текст джерелаАнотація:
Blockchain (BC) with a clustering scheme can be used to build secure and smart Vehicular Ad-Hoc Networks (VANETs), which provide improved data integrity, enhanced security, efficient resource allocation, and streamlined processes. This technology has revolutionized the transport industry by enabling safer, more efficient, and transparent transportation networks. Therefore, this paper concentrates on the design of a new Blockchain with a Quantum Mayfly Optimization-based Clustering Scheme for Secure and Smart Transport Systems (BQMFO-CSSTS) technique. The objective of the presented BQMFO-CSSTS technique is to build a secure VANET via a BC-based technology and clustering process. Moreover, the BQMFO-CSSTS technique initially uses a Quantum Mayfly Optimization (QMFO) system with a fitness function for the selection of cluster heads (CHs) and the cluster construction process. In addition, BC technology is used as trust infrastructure to provide trustworthy services to the user and protect the privacy of the CHs and cluster members (CMs). The proposed scheme leverages the decentralized and immutable nature of BC to establish trust and ensure the integrity of cluster formation in VANETs. Finally, the BQMFO-CSSTS technique uses trajectory similarity metrics to protect the integrity of the CMs against attacks. The simulation results of the BQMFO-CSSTS technique are validated using a series of measures. The comprehensive results reported the superior outcomes of the BQMFO-CSSTS method over other recent approaches, with the maximum throughput being 1644.52 kbps. Therefore, integration of BC technology provides a transparent and secure framework through which to manage cluster membership, data sharing, and trust establishment among vehicles.
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PRIGOGINE, ILYA. "WHY IRREVERSIBILITY? THE FORMULATION OF CLASSICAL AND QUANTUM MECHANICS FOR NONINTEGRABLE SYSTEMS." International Journal of Bifurcation and Chaos 05, no. 01 (February 1995): 3–16. http://dx.doi.org/10.1142/s0218127495000028.
Повний текст джерелаАнотація:
Nonintegrable Poincaré systems with continuous spectrum (so-called Large Poincaré Systems, LPS) lead to the appearance of diffusive terms in the framework of dynamics. These terms break time symmetry. They lead, therefore, to limitations to classical trajectory dynamics and of wave functions. These diffusive terms correspond to well-defined classes of dynamical processes (i.e., so-called “vacuum-vacuum” transitions). The diffusive effects are amplified in situations corresponding to persistent interactions. As a result, we have to include already in the fundamental dynamical description the two aspects, probability and irreversibility, which are so conspicuous on the macroscopic level. We have to formulate both classical and quantum mechanics on the Liouville level of probability distributions (or density matrices). For integrable systems, we recover the usual formulations of classical or quantum mechanics. Instead of being irreducible concepts, which cannot be further analyzed, trajectories and wave functions appear as special solutions of the Liouville-von Neumann equations. This extension of classical and quantum dynamics permits us to unify the two concepts of nature we inherited from the 19th century, based on the one hand on dynamical time-reversible laws and on the other on an evolutionary view associated to entropy. It leads also to a unified formulation of quantum theory avoiding the conventional dual structure based on Schrödinger’s equation on the one hand, and on the “collapse” of the wave function on the other. A dynamical interpretation is given to processes such as decoherence or approach to equilibrium without any appeal to extra dynamic considerations (such as the many-world theory, coarse graining or averaging over the environment). There is a striking parallelism between classical and quantum theory. For LPS we have, in general, both a “collapse” of trajectories and of wave functions for LPS. In both cases, we need a generalized formulation of dynamics in terms of probability distributions or density matrices. Since the beginning of this century, we know that classical mechanics had to be generalized to take into account the existence of universal constants. We now see that classical as well as quantum mechanics also have to be extended to include unstable dynamical systems such as LPS. As a result, we achieve a new formulation of "laws of physics" dealing no more with certitudes but with probabilities. The formulation is appropriate to describe an open, evolving universe.
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George, Babu, and Ontario Wooden. "Managing the Strategic Transformation of Higher Education through Artificial Intelligence." Administrative Sciences 13, no. 9 (August 29, 2023): 196. http://dx.doi.org/10.3390/admsci13090196.
Повний текст джерелаАнотація:
Considering the rapid advancements in artificial intelligence (AI) and their potential implications for the higher education sector, this article seeks to critically evaluate the strategic adoption of AI in the framework of “smart universities”. We envisage these innovative institutions as the imminent evolution in higher education, harnessing AI and quantum technologies to reshape academic and administrative processes. The core presumption is that through such integration, universities can achieve personalized learning trajectories, enhanced accessibility, economic efficiency, and a boost in overall operational performance. However, venturing into this new educational paradigm necessitates a thorough exploration of potential pitfalls, including questions surrounding educational quality, potential job losses, risks of bias, privacy breaches, and safety concerns. Our primary objective is to offer a balanced assessment to aid stakeholders in making informed strategic decisions about endorsing and advancing the smart university model. A pivotal factor in this discourse is the acceptance of qualifications from AI-enriched institutions by employers, a variable that may drastically redefine the education sector’s trajectory. Within the context of a comprehensive analysis of its broader societal impact, this article also delves into the ramifications of AI-driven innovations for historically Black colleges and universities (HBCUs).
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Ivanov S.V. "Broadening and shifting of the carbon monoxide rotational lines in a wide temperature range: calculations in the framework of the classical impact theory for CO-He." Optics and Spectroscopy 130, no. 12 (2022): 1508. http://dx.doi.org/10.21883/eos.2022.12.55235.4144-22.
Повний текст джерелаАнотація:
The classical impact theory of Gordon is used to calculate half-widths and shifts of spectral lines of the pure rotational band of 12C16O isotopologue broadened by He. Two rotational transitions are examined: J=0-> J=1 and J=1-> J=2 in the wide temperature range from 1.3 to 600 K. The main purpose of this work is the study of the validity limits of classical impact theory at low temperatures. Dynamical calculations were performed on the accurate CO-He ab initio potential energy surface. The results of calculations are in good agreement with experimental data with the exception of very low temperatures. The contributions of collisions of different types (elastic, inelastic, quasibound complexes) are clearly examined in the classical picture frame. It is shown that the mismatches between classical theory and measurements are caused by the too high contribution of elastic collisions into broadening and shift in the present variant of theoretical model. The idea in the spirit of the Weisskopf theory is applied to try to diminish this contribution. The classical results are also compared with the results of fully quantum close coupling calculations made with using four CO-He interaction potentials. The roots of discrepancies at low temperatures as well as the virtues and the shortcomings of a classical approach are discussed. Keywords: collisional line broadening and shift, intermolecular interactions, classical impact theory, classical trajectory method, quasibound complexes.
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Chough, Young-Tak. "Fock state interference: A fast computation and an analytic treatment in the frameworkof the quantum trajectory theory." Physical Review A 55, no. 4 (April 1, 1997): 3143–54. http://dx.doi.org/10.1103/physreva.55.3143.
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Ayala Oña, Roger I., Darya P. Kislyakova, and Tatyana P. Shestakova. "On the Appearance of Time in the Classical Limit of Quantum Gravity." Universe 9, no. 2 (February 5, 2023): 85. http://dx.doi.org/10.3390/universe9020085.
Повний текст джерелаАнотація:
A possible solution of the problem of time in the Wheeler–DeWitt quantum geometrodynamics is that time appears within a semiclassical limit. Following this line of thinking, one can come to the Schrodinger equation for matter fields in curved spacetime with quantum-gravitational corrections. In the present paper, we study the semiclassical limit in the case of a closed isotropic model with a scalar field decomposed into modes. We analyse calculations made within frameworks of three approaches. The first approach was proposed by Kiefer and Singh. Since the Wheeler–DeWitt equation does not contain a time derivative, it is constructed by means of a special mathematical procedure, a time variable being a parameter along a classical trajectory of gravitational field. The second method was suggested in the paper of Maniccia and Montani, who introduced the Kuchař–Torre reference fluid as an origin of time. Furthermore, the third is the extended phase space approach to the quantisation of gravity. In this approach, the temporal Schrodinger equation is argued to be more fundamental than the Wheeler–DeWitt equation, and there is no problem of time. Time is introduced due to fixing a reference frame of a certain observer, who can register the macroscopic consequences of quantum gravitational phenomena in the Very Early Universe. To go to the semiclassical limit, the Born–Oppenheimer approximation for gravity is used. In each of the approaches, in the order of O(1/M), a temporal Schrödinger equation for matter fields in curved spacetime with quantum gravitational corrections is obtained. However, equations and corrections are different in various approaches, and the results depend on the additional assumptions made within the scopes of these approaches.
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Bockler, Jessica. "Presencing with Soul." Journal of Awareness-Based Systems Change 1, no. 1 (February 25, 2021): 15–33. http://dx.doi.org/10.47061/jabsc.v1i1.471.
Повний текст джерелаАнотація:
In his outline of Theory U, an awareness-based social change methodology, Scharmer (2018) depicts seven stages of presencing which he suggests can enable deeper modes of perception and knowing, to help us actualise our highest potential for social, economic, and cultural renewal. In this paper I attempt to shine a deeper light into the seven stages of presencing, by drawing from the fields of transpersonal psychology, quantum physics, and consciousness studies. In doing so, my objective is to operationalise in psychological terms key processes in presencing, such as “letting go”, letting come”, “connecting to source”, and “dialoguing with the universe”. I explore what such processes may involve and what they may demand of presencing practitioners.
In the first half of the paper, I map Scharmer’s (2018) seven stages onto three core streams of consciousness which inform the human experience, reflecting on the features and qualities of each stream, and considering what psychosomatic dynamics may be at play as we enact the trajectory of the U. In depicting the three streams of consciousness, I highlight some of the challenges which presencing presents, suggesting that it is, in essence, a depth-psychological and spiritual approach.
In the second half of the paper, I explore the practical and ethical implications of presencing, considering what capacities and attitudes may need to be nurtured in practitioners to support skilful facilitation and enactment of the U process. I also consider what frameworks could be deployed to facilitate safe and effective practice.
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Donvil, Brecht, and Paolo Muratore-Ginanneschi. "Quantum trajectory framework for general time-local master equations." Nature Communications 13, no. 1 (July 16, 2022). http://dx.doi.org/10.1038/s41467-022-31533-8.
Повний текст джерелаАнотація:
AbstractMaster equations are one of the main avenues to study open quantum systems. When the master equation is of the Lindblad–Gorini–Kossakowski–Sudarshan form, its solution can be “unraveled in quantum trajectories” i.e., represented as an average over the realizations of a Markov process in the Hilbert space of the system. Quantum trajectories of this type are both an element of quantum measurement theory as well as a numerical tool for systems in large Hilbert spaces. We prove that general time-local and trace-preserving master equations also admit an unraveling in terms of a Markov process in the Hilbert space of the system. The crucial ingredient is to weigh averages by a probability pseudo-measure which we call the “influence martingale”. The influence martingale satisfies a 1d stochastic differential equation enslaved to the ones governing the quantum trajectories. We thus extend the existing theory without increasing the computational complexity.
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Svensson, Pontus, Thomas Campbell, Frank Graziani, Zhandos Moldabekov, Ningyi Lyu, Victor S. Batista, Scott Richardson, Sam M. Vinko, and Gianluca Gregori. "Development of a new quantum trajectory molecular dynamics framework." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 381, no. 2253 (July 2, 2023). http://dx.doi.org/10.1098/rsta.2022.0325.
Повний текст джерелаАнотація:
An extension to the wave packet description of quantum plasmas is presented, where the wave packet can be elongated in arbitrary directions. A generalized Ewald summation is constructed for the wave packet models accounting for long-range Coulomb interactions and fermionic effects are approximated by purpose-built Pauli potentials, self-consistent with the wave packets used. We demonstrate its numerical implementation with good parallel support and close to linear scaling in particle number, used for comparisons with the more common wave packet employing isotropic states. Ground state and thermal properties are compared between the models with differences occurring primarily in the electronic subsystem. Especially, the electrical conductivity of dense hydrogen is investigated where a 15% increase in DC conductivity can be seen in our wave packet model compared with other models. This article is part of the theme issue ‘Dynamic and transient processes in warm dense matter’.
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Li, Guijie, Cancan Shao, Jiabo Xu, and Linjun Wang. "A Unified Framework of Mixed Quantum-Classical Dynamics with Trajectory Branching." Journal of Chemical Physics, November 10, 2022. http://dx.doi.org/10.1063/5.0125438.
Повний текст джерелаАнотація:
As popular mixed quantum-classical dynamics methods, trajectory surface hopping (TSH) and Ehrenfest mean field (EMF) have been widely utilized to simulate nonadiabatic dynamics. Recently, we have proposed the branching corrected surface hopping (BCSH) and the branching corrected mean field (BCMF) methods, both of which closely reproduce the exact quantum dynamics in a series of standard scattering models. Here, the mixed surface hopping and mean field with branching correction (BCSHMF) is presented as a unified framework of mixed quantum-classical dynamics. As benchmarked in thousands of diverse three-level and four-level scattering models, BCSHMF achieves high reliability and flexibility, implying that surface hopping and mean field are compatible with each other in nature and trajectory branching is essential for the mixed quantum-classical description of nonadiabatic dynamics.
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Chakraborty, Madhukrishna, and Subenoy Chakraborty. "The classical and quantum implications of the Raychaudhuri Equation in f(T)-gravity." Classical and Quantum Gravity, June 27, 2023. http://dx.doi.org/10.1088/1361-6382/ace231.
Повний текст джерелаАнотація:
Abstract The present work deals with the classical and quantum aspects of the Raychaudhuri equation in the framework of f(T)-gravity theory. In the background of homogeneous and isotropic Friedmann–Lemaître–Robertson-Walker space-time, the Raychaudhuri equation has been formulated and used to examine the focusing theorem and convergence condition for different choices of f(T). Finally in quantum cosmology, the wave function of the universe has been shown to be the energy eigen function of the time-independent Schrödinger equation of a particle. Also probability measure on the mini-superspace has been examined at zero volume for singularity analysis in the quantum regime. Lastly, the Bohmian trajectory for the present quantum system has been explicitly determined for some particular choices.
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Hayashi, Yasuhiro, Takahiro Ogino, Tadakatsu Sakai, and Shigeki Sugimoto. "Stringy excited baryons in holographic quantum chromodynamics." Progress of Theoretical and Experimental Physics 2020, no. 5 (May 1, 2020). http://dx.doi.org/10.1093/ptep/ptaa045.
Повний текст джерелаАнотація:
Abstract We analyze excited baryon states using a holographic dual of quantum chromodynamics that is defined on the basis of an intersecting D4/D8-brane system. Studies of baryons in this model have been made by regarding them as a topological soliton of a gauge theory on a five-dimensional curved spacetime. However, this allows one to obtain only a certain class of baryons. We attempt to present a framework such that a whole set of excited baryons can be treated in a systematic way. This is achieved by employing the original idea of Witten, which states that a baryon is described by a system composed of $N_c$ open strings emanating from a baryon vertex. We argue that this system can be formulated by an Atiyah–Drinfeld–Hitchin–Manin-type matrix model of Hashimoto–Iizuka–Yi together with an infinite tower of the open string massive modes. Using this setup, we work out the spectra of excited baryons and compare them with the experimental data. In particular, we derive a formula for the nucleon Regge trajectory assuming that the excited nucleons lying on the trajectory are characterized by the excitation of a single open string attached on the baryon vertex.
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Choudhury, Sayantan, Ankan Dutta, and Debisree Ray. "Chaos and complexity from quantum neural network. A study with diffusion metric in machine learning." Journal of High Energy Physics 2021, no. 4 (April 2021). http://dx.doi.org/10.1007/jhep04(2021)138.
Повний текст джерелаАнотація:
Abstract In this work, our prime objective is to study the phenomena of quantum chaos and complexity in the machine learning dynamics of Quantum Neural Network (QNN). A Parameterized Quantum Circuits (PQCs) in the hybrid quantum-classical framework is introduced as a universal function approximator to perform optimization with Stochastic Gradient Descent (SGD). We employ a statistical and differential geometric approach to study the learning theory of QNN. The evolution of parametrized unitary operators is correlated with the trajectory of parameters in the Diffusion metric. We establish the parametrized version of Quantum Complexity and Quantum Chaos in terms of physically relevant quantities, which are not only essential in determining the stability, but also essential in providing a very significant lower bound to the generalization capability of QNN. We explicitly prove that when the system executes limit cycles or oscillations in the phase space, the generalization capability of QNN is maximized. Finally, we have determined the generalization capability bound on the variance of parameters of the QNN in a steady state condition using Cauchy Schwartz Inequality.
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Koessler, Eric R., Arkajit Mandal, and Pengfei Huo. "Incorporating Lindblad Decay Dynamics into Mixed Quantum-Classical Simulations." Journal of Chemical Physics, July 4, 2022. http://dx.doi.org/10.1063/5.0099922.
Повний текст джерелаАнотація:
We derive the $\mathcal{L}$-MFE method to incorporate Lindblad jump operator dynamics into the mean-field Ehrenfest (MFE) approach. We map the density matrix evolution of Lindblad dynamics onto pure state coefficients using trajectory averages. We use simple assumptions to construct the $\mathcal{L}$-MFE method that satisfies this exact mapping. This establishes a method that uses independent trajectories which exactly reproduces Lindblad decay dynamics using a wavefunction description, with deterministic changes of the magnitudes of the quantum expansion coefficients, while only adding on a stochastic phase. We further demonstrate that when including nuclei in the Ehrenfest dynamics, the $\mathcal{L}$-MFE method gives semi-quantitatively accurate results, with the accuracy limited by the accuracy of the approximations present in the semiclassical MFE approach. This work provides a general framework to incorporate Lindblad dynamics into semiclassical or mixed quantum-classical simulations.
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Ullah, Arif, and Pavlo O. Dral. "Predicting the future of excitation energy transfer in light-harvesting complex with artificial intelligence-based quantum dynamics." Nature Communications 13, no. 1 (April 11, 2022). http://dx.doi.org/10.1038/s41467-022-29621-w.
Повний текст джерелаАнотація:
AbstractExploring excitation energy transfer (EET) in light-harvesting complexes (LHCs) is essential for understanding the natural processes and design of highly-efficient photovoltaic devices. LHCs are open systems, where quantum effects may play a crucial role for almost perfect utilization of solar energy. Simulation of energy transfer with inclusion of quantum effects can be done within the framework of dissipative quantum dynamics (QD), which are computationally expensive. Thus, artificial intelligence (AI) offers itself as a tool for reducing the computational cost. Here we suggest AI-QD approach using AI to directly predict QD as a function of time and other parameters such as temperature, reorganization energy, etc., completely circumventing the need of recursive step-wise dynamics propagation in contrast to the traditional QD and alternative, recursive AI-based QD approaches. Our trajectory-learning AI-QD approach is able to predict the correct asymptotic behavior of QD at infinite time. We demonstrate AI-QD on seven-sites Fenna–Matthews–Olson (FMO) complex.
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Amati, Graziano, Johan Erik Runeson, and Jeremy O. Richardson. "On detailed balance in nonadiabatic dynamics: From spin spheres to equilibrium ellipsoids." Journal of Chemical Physics, January 19, 2023. http://dx.doi.org/10.1063/5.0137828.
Повний текст джерелаАнотація:
Trajectory-based methods that propagate classical nuclei on multiple quantum electronic states are often used to simulate nonadiabatic processes in the condensed phase. A long-standing problem of these methods is their lack of detailed balance, meaning that they do not conserve the equilibrium distribution. In this article, we investigate ideas for how to restore detailed balance in mixed quantum-classical systems by tailoring the previously proposed spin-mapping approach to thermal equilibrium. We find that adapting the spin magnitude can recover the correct long-time populations but is insufficient to conserve the full equilibrium distribution. The latter can however be achieved by a more flexible mapping of the spin onto an ellipsoid, which is constructed to fulfill detailed balance for arbitrary potentials. This ellipsoid approach solves the problem of negative populations that has plagued previous mapping approaches and can therefore be applied also to strongly asymmetric and anharmonic systems. Because it conserves the thermal distribution, the method can also exploit efficient sampling schemes used in standard molecular dynamics, which drastically reduces the number of trajectories needed for convergence. The dynamics does however still have mean-field character, as is observed most clearly by evaluating reaction rates in the golden-rule limit. This implies that although the ellipsoid mapping provides a rigorous framework, further work is required to find an accurate classical-trajectory approximation that captures more properties of the true quantum dynamics.
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Mannouch, Jonathan Richard, and Jeremy O. Richardson. "A mapping approach to surface hopping." Journal of Chemical Physics, February 20, 2023. http://dx.doi.org/10.1063/5.0139734.
Повний текст джерелаАнотація:
We present a nonadiabatic classical-trajectory approach that offers the best of both worlds between fewest-switches surface hopping (FSSH) and quasiclassical mapping dynamics. This mapping approach to surface hopping (MASH) propagates the nuclei on the active adiabatic potential-energy surface, like in FSSH. However, unlike in FSSH, transitions between active surfaces are deterministic and occur when the electronic mapping variables evolve between specified regions of the electronic phase space. This guarantees internal consistency between the active surface and the electronic degrees of freedom throughout the dynamics. MASH is rigorously derivable from exact quantum mechanics as a limit of the quantum-classical Liouville equation (QCLE), leading to a unique prescription for momentum rescaling and frustrated hops. Hence, a quantum-jump procedure can in principle be used to systematically converge the accuracy of the results to that of the QCLE. This jump procedure also provides a rigorous framework for deriving approximate decoherence corrections similar to those proposed for FSSH. We apply MASH to simulate the nonadiabatic dynamics in various model systems and show that it consistently produces more accurate results than FSSH at a comparable computational cost.
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Vancea, Ion. "Semiclassical bosonic D-brane boundary states in curved spacetime." Open Physics 8, no. 1 (January 1, 2010). http://dx.doi.org/10.2478/s11534-009-0084-y.
Повний текст джерелаАнотація:
AbstractIn this paper we discuss the existence of quantum D-brane states in the strong gravitational field and in the presence of a constant Kalb-Ramond field. A semiclassical string quantization method in which the spacetime metric g AB and the constant antisymmetric Kalb-Ramond field b AB are treated exactly is employed. In this framework, the semiclassical D-branes are defined at the first order perturbation around the trajectory of the center-of-mass of a string. The set of equations the semiclassical D-branes must satisfy in a general strong gravitational field are given. These equations are solved in the AdS background where it is shown that a D-brane coherent state exists if the operators that project the string fields onto the corresponding Neumann and Dirichlet directions satisfy a set of algebraic constraints. A second set of equations that should be satisfied by the projectors in order that the semiclassical state be compatible with the global structure of the D-brane are derived in the particle limit of a string in the torsionless AdS background.