Understanding quantum work in a quantum many-body system

Abstract

Based on previous studies in a single-particle system in both the integrable [Jarzynski, Quan, and Rahav, Phys. Rev. X 5, 031038 (2015)] and the chaotic systems [Zhu, Gong, Wu, and Quan, Phys. Rev. E 93, 062108 (2016)], we study the the correspondence principle between quantum and classical work distributions in a quantum many-body system. Even though the interaction and the indistinguishability of identical particles increase the complexity of the system, we find that for a quantum many-body system the quantum work distribution still converges to its classical counterpart in the semiclassical limit. Our results imply that there exists a correspondence principle between quantum and classical work distributions in an interacting quantum many-body system, especially in the large particle number limit, and further justify the definition of quantum work via two-point energy measurements in quantum many-body systems.

Quantum work statistics and resource theories: Bridging the gap through Rényi divergences

“…In such a framework, the statistics of stochastic thermodynamic variables can be gathered through two-time projectivemeasurement protocols, where the fluctuating work done by or on a system driven out of equilibrium or the heat that it exchanges with an environment are defined in terms of the difference of energy eigenvalues observed at the start and the end of the dynamics [10,11]. This approach is experimentally viable [12,13], has been useful for the characterization of nonequilibrium features of quenched many-body systems [14][15][16][17][18] and there is strong evidence that it has a physically meaningful semi-classical limit [19][20][21][22][23].…”

“…from which, by simply using the definition of work given by the energy difference in the battery W = E B (0) − E B (τ ), we obtain Eq. (21).…”

Computing characteristic functions of quantum work in phase space

“…In the remainder of this section, we apply Eqs. (15) and (17) to compute the CFs of three quantum systems composed of harmonic oscillators.…”

Decoherence approach to energy transfer and work done by slowly driven systems

“…A merit of this definition is that the statistics of work complies with the fluctuation theorems of Jarzynski [5] and Crooks [6]. Recently, this definition is further justified from the angle of the quantum-classical correspondence principle in integrable [7], chaotic [8], and many-body systems [9].…”