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物性研究

Is entanglement quantum?(Perspectives of Nonequilibrium Statistical Physics-The Memory of Professor Shuichi Tasaki-)

Paolo Facchi A, Saverio Pascazio

Published Dec 5, 2011• 0 citations
OpenAlex

Abstract

Shuichi Tasaki was a very talented physicist.He would perform very complicated calculations in very short times.He would work everywhere, even late in the evening, going home.If you happened to meet him in the train, chances were high that he would not "see" you, absorbed as he was in his physics problems.Shuichi liked all branches of physics, with no exceptions.However, two subjects attracted him most: second-order calculations in the weak coupling limit, leading to markovianity, and the C* algebraic approach to quantum field theory and statistical mechanics.This article focuses on the latter.It is a pleasure to dedicate it to Shuichi.

Related papers

Quantum statistical mechanics in infinitely extended systems : C[*] algebraic approach (Perspectives of Nonequilibrium Statistical Physics : The Memory of Professor Shuichi Tasaki)

Shuichi Tasaki, Shigeru Ajisaka, Felipe Barra

This is a lecture note of Professor Shuichi Tasaki. In the last part of this manuscript, SA and FB demonstrate some recent results as well. As far as SA's knowledge, regular courses were given every two years for graduate students at Waseda university, and SA attended the course twice (probably in 2005 and 2007 or in 2006 and 2008). Some topics were added in the lectures of the later year, probably Professor Tasaki modified his lectures as he was discovering new results. A similar but intensive short course was given once as at Kyoto university. SA thinks Professor Tasaki had a unique philosophy of physics, which enabled him to give very attractive lectures that unfortunately it is not possible to attend any more. In Professor Tasaki's lectures, both beautiful mathematical views and clear physical intuition were always given together, which SA believe, is quite difficult. As many people know Professor Tasaki was very strong in mathematics, but he never forgot to think of physical interpretations. Professor Tasaki was writing a lecture note of this course based on the note taken by a student of Kyoto university. Unfortunately, Prof. Tasaki passed away before he finished writing the manuscript. This lecture note is based on the incomplete Japanese note[1] and a note taken by SA at Waseda university. It seems that main stories of the lectures are the same, but Professor Tasaki gave different materials in detail, and use different notations. This manuscript mainly follows the note of SA. SA and FB decided to write this manuscript (1) to complete a note of Professor Tasaki's lectures, and (2) to give an access for non-Japanese speaker to his lecture note. However, they are slow writer, and they could not finish it before the deadline of this volume. They could finish only parts before nonequilibrium states (only some of the results will be shown in this version), and some recent results about Landauer formula and sufficient condition on interaction for the existence of unique steady states. They hope to complete the lecture note part, and upload it on Arxiv in the future.

物性研究•Dec 5, 2011•0 citations

Universal Characteristics of Time-irreversibility in Quantum Normal Diffusion(Perspectives of Nonequilibrium Statistical Physics-The Memory of Professor Shuichi Tasaki-)

Hiroaki S. Yamada, Kensuke S. Ikeda

Time-irreversibility of apparently irreversible phenomena observed in quantum systems with a very small number of degrees of freedom is studied quantitatively by a time-reversal test: the system evolved in the forward-time direction is time-reversed after applying a small perturbation at the reversal time and the separation between the time-reversed perturbed and the time-reversed unperturbed states is measured as a function of perturbation strength. If the system exhibits a normal diffusion, the time-reversal characteristics has a universal threshold of perturbation strength above which a complete loss of memory is realized. A remarkable fact is that, for almost all the model systems we examined, including discrete-time/continuous-time systems and deterministic/stochastic systems, the time reversal characteristics as well as the time-reversal dynamics itself converge asymptotically to universal behaviors independent of the details of the systems, which implies the prototype of quantum irreversibility. Only the diffusive behavior of the critical states in Harper equation deviates significantly from the universal behavior.

物性研究•Dec 5, 2011•0 citations

Relaxation to equilibrium in macroscopic quantum systems : foundation of statistical mechanics(Perspectives of Nonequilibrium Statistical Physics-The Memory of Professor Shuichi Tasaki-)

Takaaki Monnai

In conclusion, by assuming that the initial state is prepared as a microcanonical ensemble, the actual state at time t=T can be replaced by another microcanonical ensemble in the evaluation of macroscopic quantities. The derivation is based on the high dimensionality of the Hilbert space, and restrictions for the system size dependence of observables as well as the perturbative treatment of the unitary transformation of the energy eigenstates. The validity of the uniformly random sampling assumption for [numerical formula] is numerically verified for a nonintegrable spin chain. It is also remarked that the initial state can be out of equilibrium, i.e. the initial density matrix is [numerical formula] with a unitary transformation U_0, since this can be regarded as the state evolved from an actual initial state [numerical formula].

物性研究•Dec 5, 2011•0 citations

Canonical Ensemble of Noninteracting Bosonic Atoms and Interference of Bose-Einstein Condensates(Perspectives of Nonequilibrium Statistical Physics-The Memory of Professor Shuichi Tasaki-)

Kazuya Yuasa

We have discussed the interference of two independently prepared Bose-Einstein condensates. When the number of atoms in each gas is fixed and the phases of the gases are uncertain, no interference is expected in the single-particle distribution. However, the interference is observed in each single snapshot. We have presented tools for studying such snapshot interference, the measurement-induced interference. The idea is to discard the randomness in the snapshot profiles (the spatial offsets of the interference patterns) and to focus on the typical feature in the interference patterns (the fringe spacing). If the sinusoidal patterns with a definite fringe spacing is actually typical, the fringe spectrum with the random offset discarded does not fluctuate, and we are allowed to speak of the snapshot interference through its average. We have described the two gases as canonical ensembles with the numbers of atoms fixed at N individually. We have shown that the covariance of the fringe spectrum over all possible snapshot profiles is vanishingly small below the critical temperature of the Bose-Einstein condensation: the interference pattern whose fringe contrast is characterized by the average fringe spectrum is certainly observed in every snapshot in the presence of condensates. The fringe contrast becomes stronger as the temperature is lowered and the condensation fraction is increased. This clarifies the importance of the Bose-Einstein condensation to the interference of independent Bose-Einstein condensates. The knowledge I acquired from Prof. Tasaki's lecture on how to characterize the canonical ensemble of bosonic atoms has enabled us to carry out this analysis. Like this example, the coherence phenomena of quantum many-body systems in general would be explained on the basis of the idea of the measurement-indued coherence, without resort to the idea of the spontaneous symmetry breaking. This is actually true also for fermionic systems: the relative phase between two independent superconductors is built up by measurement, even though their U(1) symmetries are not broken and their phases are uncertain beforehand. It would be interesting to explore the possibility of explaining various phenomena, in which the symmetry breaking plays an essential role, on the basis of the measurement-induced coherence.

物性研究•Dec 5, 2011•0 citations

Gaussian, exponential and power-law decays and their time ranges : An analysis based on the Friedrichs model(Perspectives of Nonequilibrium Statistical Physics-The Memory of Professor Shuichi Tasaki-)

Hiromichi Nakazato

The time ranges of the three typical decay forms in quantum mechanics, i.e., the Gaussian, exponential and power-law decays, are investigated on the basis of the Friedrichs model. The analysis yields a deeper understanding of the decay dynamics of quantum systems.

物性研究•Dec 5, 2011•0 citations

Quantum statistical mechanics

Mehran Kardar A

Statistical physics has its origins in attempts to describe the thermal properties of matter in terms of its constituent particles, and has played a fundamental role in the development of quantum mechanics. Based on lectures taught by Professor Kardar at MIT, this textbook introduces the central concepts and tools of statistical physics. It contains a chapter on probability and related issues such as the central limit theorem and information theory, and covers interacting particles, with an extensive description of the van der Waals equation and its derivation by mean field approximation. It also contains an integrated set of problems, with solutions to selected problems at the end of the book and a complete set of solutions is available to lecturers on a password protected website at www.cambridge.org/9780521873420. A companion volume, Statistical Physics of Fields, discusses non-mean field aspects of scaling and critical phenomena, through the perspective of renormalization group.

Cambridge University Press eBooks•Jun 7, 2007•0 citations
Shuichi Tasaki was a very talented physicist.He would perform very complicated calculations in very short times.He would work everywhere, even late in the evening, going home.If you happened to meet him in the train, chances were high that he would not "see" you, absorbed as he was in his physics problems.Shuichi liked all branches of physics, with no exceptions.However, two subjects attracted him most: second-order calculations in the weak coupling limit, leading to markovianity, and the C* algebraic approach to quantum field theory and statistical mechanics.This article focuses on the latter.It is a pleasure to dedicate it to Shuichi.
This is a lecture note of Professor Shuichi Tasaki. In the last part of this manuscript, SA and FB demonstrate some recent results as well. As far as SA's knowledge, regular courses were given every two years for graduate students at Waseda university, and SA attended the course twice (probably in 2005 and 2007 or in 2006 and 2008). Some topics were added in the lectures of the later year, probably Professor Tasaki modified his lectures as he was discovering new results. A similar but intensive short course was given once as at Kyoto university. SA thinks Professor Tasaki had a unique philosophy of physics, which enabled him to give very attractive lectures that unfortunately it is not possible to attend any more. In Professor Tasaki's lectures, both beautiful mathematical views and clear physical intuition were always given together, which SA believe, is quite difficult. As many people know Professor Tasaki was very strong in mathematics, but he never forgot to think of physical interpretations. Professor Tasaki was writing a lecture note of this course based on the note taken by a student of Kyoto university. Unfortunately, Prof. Tasaki passed away before he finished writing the manuscript. This lecture note is based on the incomplete Japanese note[1] and a note taken by SA at Waseda university. It seems that main stories of the lectures are the same, but Professor Tasaki gave different materials in detail, and use different notations. This manuscript mainly follows the note of SA. SA and FB decided to write this manuscript (1) to complete a note of Professor Tasaki's lectures, and (2) to give an access for non-Japanese speaker to his lecture note. However, they are slow writer, and they could not finish it before the deadline of this volume. They could finish only parts before nonequilibrium states (only some of the results will be shown in this version), and some recent results about Landauer formula and sufficient condition on interaction for the existence of unique steady states. They hope to complete the lecture note part, and upload it on Arxiv in the future.
Time-irreversibility of apparently irreversible phenomena observed in quantum systems with a very small number of degrees of freedom is studied quantitatively by a time-reversal test: the system evolved in the forward-time direction is time-reversed after applying a small perturbation at the reversal time and the separation between the time-reversed perturbed and the time-reversed unperturbed states is measured as a function of perturbation strength. If the system exhibits a normal diffusion, the time-reversal characteristics has a universal threshold of perturbation strength above which a complete loss of memory is realized. A remarkable fact is that, for almost all the model systems we examined, including discrete-time/continuous-time systems and deterministic/stochastic systems, the time reversal characteristics as well as the time-reversal dynamics itself converge asymptotically to universal behaviors independent of the details of the systems, which implies the prototype of quantum irreversibility. Only the diffusive behavior of the critical states in Harper equation deviates significantly from the universal behavior.
In conclusion, by assuming that the initial state is prepared as a microcanonical ensemble, the actual state at time t=T can be replaced by another microcanonical ensemble in the evaluation of macroscopic quantities. The derivation is based on the high dimensionality of the Hilbert space, and restrictions for the system size dependence of observables as well as the perturbative treatment of the unitary transformation of the energy eigenstates. The validity of the uniformly random sampling assumption for [numerical formula] is numerically verified for a nonintegrable spin chain. It is also remarked that the initial state can be out of equilibrium, i.e. the initial density matrix is [numerical formula] with a unitary transformation U_0, since this can be regarded as the state evolved from an actual initial state [numerical formula].
We have discussed the interference of two independently prepared Bose-Einstein condensates. When the number of atoms in each gas is fixed and the phases of the gases are uncertain, no interference is expected in the single-particle distribution. However, the interference is observed in each single snapshot. We have presented tools for studying such snapshot interference, the measurement-induced interference. The idea is to discard the randomness in the snapshot profiles (the spatial offsets of the interference patterns) and to focus on the typical feature in the interference patterns (the fringe spacing). If the sinusoidal patterns with a definite fringe spacing is actually typical, the fringe spectrum with the random offset discarded does not fluctuate, and we are allowed to speak of the snapshot interference through its average. We have described the two gases as canonical ensembles with the numbers of atoms fixed at N individually. We have shown that the covariance of the fringe spectrum over all possible snapshot profiles is vanishingly small below the critical temperature of the Bose-Einstein condensation: the interference pattern whose fringe contrast is characterized by the average fringe spectrum is certainly observed in every snapshot in the presence of condensates. The fringe contrast becomes stronger as the temperature is lowered and the condensation fraction is increased. This clarifies the importance of the Bose-Einstein condensation to the interference of independent Bose-Einstein condensates. The knowledge I acquired from Prof. Tasaki's lecture on how to characterize the canonical ensemble of bosonic atoms has enabled us to carry out this analysis. Like this example, the coherence phenomena of quantum many-body systems in general would be explained on the basis of the idea of the measurement-indued coherence, without resort to the idea of the spontaneous symmetry breaking. This is actually true also for fermionic systems: the relative phase between two independent superconductors is built up by measurement, even though their U(1) symmetries are not broken and their phases are uncertain beforehand. It would be interesting to explore the possibility of explaining various phenomena, in which the symmetry breaking plays an essential role, on the basis of the measurement-induced coherence.
Statistical physics has its origins in attempts to describe the thermal properties of matter in terms of its constituent particles, and has played a fundamental role in the development of quantum mechanics. Based on lectures taught by Professor Kardar at MIT, this textbook introduces the central concepts and tools of statistical physics. It contains a chapter on probability and related issues such as the central limit theorem and information theory, and covers interacting particles, with an extensive description of the van der Waals equation and its derivation by mean field approximation. It also contains an integrated set of problems, with solutions to selected problems at the end of the book and a complete set of solutions is available to lecturers on a password protected website at www.cambridge.org/9780521873420. A companion volume, Statistical Physics of Fields, discusses non-mean field aspects of scaling and critical phenomena, through the perspective of renormalization group.