Quantum ergodicity for a class of non-generic systems

Asadi, Pouya; Bakhshinezhad, Faraj; Rezakhani, A. T.

doi:10.1088/1751-8113/49/5/055301

Cited by 6 publications

(4 citation statements)

References 40 publications

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“…He has hence defined quantum ergodicity by the equality of the time average of an arbitrary quantum operator and its ensemble average. More recently, in [7,8] quantum ergodicity has been studied in terms of the energy structure of the system, namely its eigenenergies and energy spacings. The absence of degeneracies then leads to the ergodic property of coinciding time and ensemble averages, without involving the notion of quantum chaos.…”

Section: Introductionmentioning

confidence: 99%

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Ergodicity in randomly perturbed quantum systems

Gherardini¹,

Lovecchio²,

Müller³

et al. 2017

Quantum Sci. Technol.

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The theoretical cornerstone of statistical mechanics is the ergodic assumption, i.e. the assumption that the time average of an observable equals its ensemble average. Here, we show how such a property is present when an open quantum system is continuously perturbed by an external environment effectively observing the system at random times while the system dynamics approaches the quantum Zeno regime. In this context, by large deviation theory we analytically show how the most probable value of the probability for the system to be in a given state eventually deviates from the non-stochastic case when the Zeno condition is not satisfied. We experimentally test our results with ultra-cold atoms prepared on an atom chip.

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Section: Introductionmentioning

confidence: 99%

“…More recently, in Refs. [5,6] quantum ergodicity has been examined using the energy structure of the system, namely its eigenenergies and energy spacings, while in [7] ergodic dynamics has been proved in a small quantum system consisting of only three superconducting qubits, as a general framework for investigating non-equilibrium thermodynamics.…”

mentioning

confidence: 99%

Ergodicity in randomly perturbed quantum systems

Gherardini¹,

Lovecchio²,

Müller³

et al. 2017

Quantum Sci. Technol.

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“…[4] uncomputable. Though there may be some revisions to the theorem [16], this difficulty is not overcome.…”

Section: Introductionmentioning

confidence: 99%

Ergodicity and mixing in quantum dynamics

Zhang

Quan

2016

Phys. Rev. E

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After a brief historical review of ergodicity and mixing in dynamics, particularly in quantum dynamics, we introduce definitions of quantum ergodicity and mixing using the structure of the system's energy levels and spacings. Our definitions are consistent with the usual understanding of ergodicity and mixing. Two parameters concerning the degeneracy in energy levels and spacings are introduced. They are computed for right triangular billiards and the results indicate a very close relation between quantum ergodicity (mixing) and quantum chaos. At the end, we argue that, besides ergodicity and mixing, there may exist a third class of quantum dynamics which is characterized by a maximized entropy.

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“…More precisely, the wave function of a closed system is contained on the surface of the hyper-sphere that is given by the decomposition of the wave function into eigenvectors of the Hamiltonian, and the system is then ergodic on this hypersphere[19,45]. The details of quantum ergodicity are still a topic of ongoing research[46][47][48][49][50][51][52].…”

mentioning

confidence: 99%

Quantum coarse-grained entropy and thermalization in closed systems

Šafránek,

Deutsch,

Aguirre

2018

Preprint

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We investigate the detailed properties of Observational entropy, introduced by Šafránek et al. [Phys. Rev. A 99, 010101 (2019)] as a generalization of Boltzmann entropy to quantum mechanics. This quantity can involve multiple coarse-grainings, even those that do not commute with each other, without losing any of its properties. It is well-defined out of equilibrium, and for some coarse-grainings it generically rises to the correct thermodynamic value even in a genuinely isolated quantum system. The quantity contains several other entropy definitions as special cases, it has interesting information-theoretic interpretations, and mathematical properties -such as extensivity and upper and lower bounds -suitable for an entropy. Here we describe and provide proofs for many of its properties, discuss its interpretation and connection to other quantities, and provide numerous simulations and analytic arguments supporting the claims of its relationship to thermodynamic entropy. This quantity may thus provide a clear and well-defined foundation on which to build a satisfactory understanding of the second thermodynamical law in quantum mechanics.

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Quantum ergodicity for a class of non-generic systems

Cited by 6 publications

References 40 publications

Ergodicity in randomly perturbed quantum systems

Ergodicity in randomly perturbed quantum systems

Ergodicity and mixing in quantum dynamics

Quantum coarse-grained entropy and thermalization in closed systems

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