Quantum work for sudden quenches in Gaussian random Hamiltonians

Abstract

In the context of nonequilibrium quantum thermodynamics, variables like work behave stochastically. A particular definition of the work probability density function (pdf) for coherent quantum processes allows the verification of the quantum version of the celebrated fluctuation theorems, due to Jarzynski and Crooks, that apply when the system is driven away from an initial equilibrium thermal state. Such a particular pdf depends basically on the details of the initial and final Hamiltonians, on the temperature of the initial thermal state and on how some external parameter is changed during the coherent process. Using random matrix theory we derive a simple analytic expression that describes the general behavior of the work characteristic function $G(u)$, associated with this particular work pdf for sudden quenches, valid for all the traditional Gaussian ensembles of Hamiltonians matrices. This formula well describes the general behavior of $G(u)$ calculated from single draws of the initial and final Hamiltonians in all ranges of temperatures.

arXiv comment9 pages, 3 figures, Accepted to be published in Physical Review E

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• Spectral Filtering Induced by Non-Hermitian Evolution with Balanced Gain and Loss: Enhancing Quantum Chaos
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• Quantum coherence and criticality in irreversible work
• Work statistics for sudden quenches in interacting quantum many-body systems
• Partial Fermionization---Spectral Universality in 1D Repulsive Bose Gases
• Theory of Quantum Work in Metallic Grains
• Classical Theory of Quantum Work Distribution in Chaotic Fermion Systems
• Superdiffusive quantum work and adiabatic quantum evolution in finite temperature chaotic Fermi systems
• Irreversible Work Reduction by Disorder in Many-Body Quantum Systems
• Work and heat exchanged during sudden quenches of strongly coupled quantum systems