Many-body effects on the thermodynamics of closed quantum systems

Abstract

Thermodynamics of quantum systems out-of-equilibrium is very important for the progress of quantum technologies, however, the effects of many body interactions and their interplay with temperature, different drives and dynamical regimes is still largely unknown. Here we present a systematic study of these interplays: we consider a variety of interaction (from non-interacting to strongly correlated) and dynamical (from sudden quench to quasi-adiabatic) regimes, and draw some general conclusions in relation to work extraction and entropy production. As treatment of many-body interacting systems is highly challenging, we introduce a simple approximation which includes, for the average quantum work, many-body interactions only via the initial state, while the dynamics is fully non-interacting. We demonstrate that this simple approximation is surprisingly good for estimating both the average quantum work and the related entropy variation, even when many-body correlations are significant.

Approximating quantum thermodynamic properties using DFT

“…We consider systems with N = 6; for each site i, µ 0 i = µ 0 (−1) i at t = 0 and µ τ i = µ τ (−1) i at t = τ , where µ 0 = 0.5J and µ τ = 4.5J ('Comb' potential [19]). These chains and dynamics are directly comparable to the ones in reference [19] 1.…”

“…We consider systems with N = 6; for each site i, µ 0 i = µ 0 (−1) i at t = 0 and µ τ i = µ τ (−1) i at t = τ , where µ 0 = 0.5J and µ τ = 4.5J ('Comb' potential [19]). These chains and dynamics are directly comparable to the ones in reference [19] 1. Metallic, Mott insulator and band insulator phases equation 5 with the 'comb' potential describes an ionic Hubbard model (see e.g.…”

“…As the exchange-correlation and Hartree potentials are only calculated at t = 0 as derived from the ground state theory, calculations remain "cheap". This is still a relatively crude approximation to the many-body dynamics, but constitutes the next step towards including interactions within the system dynamics with respect to Reference [19].…”

“…The development and applications of DFT to finite temperature problems [23], and especially to finitetemperature systems out-of equilibrium, are comparatively still in their infancy. Hence the importance of the present study, in which we combine and adapt some well-known zero-temperature, DFT approximations for model Hamiltonians with the 'hybrid' approach from reference [19] and test their limits in describing the quantum thermodynamics of finite-temperature systems strongly out of equilibrium. This work will complement and extend the recent work [24] which considered static systems and showed that approximations to the exchangecorrelation potential built for ground-states should be accurate at finite T below a characteristic thermal scale associated with the Fermi energy.…”

Easy Access to Energy Fluctuations in Nonequilibrium Quantum Many-Body Systems

“…An efficient protocol to experimentally investigate energy fluctuations in a general out-of-equilibrium many-body system remains an outstanding challenge: the aim of this letter is to provide a long stride towards this goal by introducing a fresh approach. Previously we developed methods inspired by density-functional-theory (DFT [20]) [21][22][23] to support numerical calculations of energy fluctuations for out-ofequilibrium many-body system, a tough problem in itself; here we focus on providing directly an experimental method for measuring these quantities.…”