Current fluctuations in general open quantum systems and crossover to the isolated thermodynamic limit

Neha Pathania, Devvrat Tiwari, Subhashish Banerjee

Archak Purkayastha

Abstract There are two standard ways of classifying transport behavior of systems. The first is via time scaling of spread of correlations in the isolated system in thermodynamic limit. The second is via system size scaling of conductance in the steady state of the open system. We show here that these correspond to taking the thermodynamic limit and the long time limit of the integrated equilibrium current–current correlations of the open system in different order. In general, the limits may not commute leading to a conflict between the two standard ways of transport classification. Nevertheless, the full information is contained in the equilibrium current–current correlations of the open system. We show this analytically by rigorously deriving the open-system current fluctuation dissipation relations starting from an extremely general open quantum set-up and then carefully taking the proper limits. We test our theory numerically on the non-trivial example of the critical Aubry–André–Harper model, where, it has been recently shown that, the two standard classifications indeed give different results. We find that both the total current autocorrelation and the long-range local current correlations of the open system in equilibrium show signatures of diffusive transport up to a time scale. This time scale grows as square of system size. Beyond this time scale a steady state value is reached. The steady state value is conductance, which shows sub-diffusive scaling with system size.

Juliette Monsel

Alessandra Colla, Andrea Smirne, Heinz-Peter Breuer +1 more

We propose a method to evaluate general thermodynamic fluctuations in open quantum systems, based on performing a two-point measurement scheme on the system using dynamics-dependent thermodynamic observables. Our approach allows one to obtain exact equalities for fluctuations of path-dependent thermodynamic quantities such as work and heat, and to isolate correction factors to Jarzynski's equality, requiring only access to the system degrees of freedom. This framework is flexible and can be applied to the limiting case of closed systems, recovering previous, yet seemingly contradictory, results from the literature. Moreover, the formalism admits a straightforward extension to strongly coupled open quantum systems. We investigate the effect of specific dynamical classes on the fluctuation relations, and show that the pure decoherence case is particularly special, as it deterministically does not contain any heat contribution and thus constitutes a class of open system dynamics for which the Jarzynski equality for work fluctuations is identically true at any coupling strength. Finally, we look explicitly at the shape and size of the correction factors to Jarzynski's equality for a qubit undergoing phase covariant dynamics, both in the weakly-coupled regime and in the deep non-Markovian regime.

Benjamin W. Schumacher, Michael D. Westmoreland, Alexander New +1 more

This paper explores the generalization of the concept of a "probability current", familiar from wave-function quantum mechanics, to quantum systems with finite-dimensional Hilbert spaces. The generalized definition applies both to isolated systems evolving via the Schrödinger equation and to more general open systems obeying the Lindblad master equation. We establish several properties of the probability current and explore its relation to thermodynamic heat and work.

Madhukar Mallayya Krishnanand