Work distributions for random sudden quantum quenches

Łobejko, Marcin; Łuczka, J.; Talkner, Peter

doi:10.1103/physreve.95.052137

Cited by 24 publications

(29 citation statements)

References 31 publications

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“…For high temperature (β 1), the exact asymptotic behavior is thus (23) verifying the fact that the mean work vanishes exactly in the infinite temperature limit and increases as the temperature is decreased, as seen in Figure 2. The mean work is lower-bounded by the low-temperature limit,…”

Section: Mean Work In a Random Quenchsupporting

confidence: 59%

“…(13). While the average of the transition probabilities generates a uniform distribution, known as p τ m|n θ 0 ,θ τ = 1/N [23], the average of two transition probabilities is quite more involved and has not yet been reported. The difficulty in evaluating this expression comes from the fact that the second transition is not independent from the first one, creating a complex combinational problem.…”

Section: A Loschmidt Echo Averaged Over the Guementioning

confidence: 99%

“…Quantum chaos plays as well a prominent role in black hole physics, as it is widely believed that quantum correlations in these systems are scrambled at a maximum rate saturating an analogue of the Lyapunov exponent [21]. It should be noted that, very recently, preliminary steps have been taken to study work statistics in quantum chaotic systems [22][23][24].…”

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confidence: 99%

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Work Statistics, Loschmidt Echo and Information Scrambling in Chaotic Quantum Systems

Chenu

Molina-Vilaplana

Campo

2019

Quantum

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Characterizing the work statistics of driven complex quantum systems is generally challenging because of the exponential growth with the system size of the number of transitions involved between different energy levels. We consider the quantum work distribution associated with the driving of chaotic quantum systems described by random matrix Hamiltonians and characterize exactly the work statistics associated with a sudden quench for arbitrary temperature and system size. Knowledge of the work statistics yields the Loschmidt echo dynamics of an entangled state between two copies of the system of interest, the thermofield double state. This echo dynamics is dictated by the spectral form factor. We discuss its relation to frame potentials and its use to assess information scrambling.Quantum thermodynamics has become a research field in bloom, building on the dialogue between technological progress and foundations of physics [1,2]. In the presence of thermal and quantum fluctuations, familiar concepts from traditional thermodynamics at the macroscale, such as heat and work, become stochastic variables. Their analysis has been a fertile ground of inquiry, leading to the discovery of fluctuation theorems [3][4][5][6][7] and time-work uncertainty relations [8][9][10].In the quantum domain, even for isolated systems governed by unitary dynamics, work is not considered to be an observable. The definition of work requires two projective measurements, one at the beginning and another at the end of the physical pro-Aurélia Chenu: achenu@dipc.org,

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Section: Mean Work In a Random Quenchsupporting

confidence: 59%

Section: A Loschmidt Echo Averaged Over the Guementioning

confidence: 99%

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Work Statistics, Loschmidt Echo and Information Scrambling in Chaotic Quantum Systems

Chenu

Molina-Vilaplana

Campo

2019

Quantum

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“…This transition was already been observed in different spin-1/2 chain models [50]. Also we remark that RMT have brought new insights to quantum thermodynamics [52][53][54], with special attention devoted to the work distribution function [52,53,55,56] and information scrambling [56,57].…”

Section: Introductionsupporting

confidence: 66%

Work statistics for sudden quenches in interacting quantum many-body systems

et al. 2019

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Work in isolated systems, defined by the two projective energy measurement scheme, is a random variable whose the distribution function obeys the celebrated fluctuation theorems of Crooks and Jarzynski. In this study, we provide a simple way to calculate the work distribution associated to sudden quench processes in a given class of quantum many-body systems. Due to the large Hilbert space dimension of these systems, we show that there is an energy coarse-grained description of the exact work distribution that can be constructed from two elements: the level density of the initial Hamiltonian, and the strength function, which provides information about the influence of the perturbation over the eigenvectors in the quench process. We also show how random Hamiltonian models can be helpful to find the energy coarse-grained work probability distribution and apply this approach to different spin-1/2 chain models. Our finding provides an accurate description of the work distribution of such systems in the cases of intermediate and high temperatures in both chaotic and integrable regimes.arXiv:1907.06285v1 [quant-ph]

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“…The Hamiltonians we consider are random N × N Hermitian matrices sampled from the Gaussian Orthogonal Ensemble (GOE) 45 , which are invariant under time reversal. A sudden random quench can be implemented by choosing the initial and final Hamiltonians,Ĥ 0 =Ĥ i and H τ =Ĥ f , from two independent GOE 46 . The corresponding characteristic function averaged over the GOE…”

Section: Quantum Work Statistics Of Quantum Chaotic Systemsmentioning

confidence: 99%

Quantum work statistics, Loschmidt echo and information scrambling

Chenu¹,

Egusquiza²,

Molina-Vilaplana³

et al. 2018

Sci Rep

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A universal relation is established between the quantum work probability distribution of an isolated driven quantum system and the Loschmidt echo dynamics of a two-mode squeezed state. When the initial density matrix is canonical, the Loschmidt echo of the purified double thermofield state provides a direct measure of information scrambling and can be related to the analytic continuation of the partition function. Information scrambling is then described by the quantum work statistics associated with the time-reversal operation on a single copy, associated with the sudden negation of the system Hamiltonian.

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Work distributions for random sudden quantum quenches

Cited by 24 publications

References 31 publications

Work Statistics, Loschmidt Echo and Information Scrambling in Chaotic Quantum Systems

Work Statistics, Loschmidt Echo and Information Scrambling in Chaotic Quantum Systems

Work statistics for sudden quenches in interacting quantum many-body systems

Quantum work statistics, Loschmidt echo and information scrambling

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