Work Statistics and Adiabatic Assumption in Nonequilibrium Many-Body Theory

TL;DR

This paper investigates the limitations of adiabatic assumptions in Keldysh field theory for nonequilibrium many-body systems, revealing when adiabatic evolutions fail or succeed in transforming Gibbs states, with implications for quantum state preparation.

Contribution

It introduces a universal theorem characterizing evolutions between Gibbs states and analytically shows the failure of adiabatic methods in certain interacting systems, supported by numerical verification.

Findings

Adiabatic evolutions cannot transform non-interacting Gibbs states into interacting ones.

Adiabatic approximations are generally better than non-adiabatic ones.

Numerical results support the theoretical predictions.

Abstract

Keldysh field theory, based on adiabatic assumptions, serves as an widely used framework for addressing nonequilibrium many-body systems. Nonetheless, the validity of such adiabatic assumptions when addressing interacting Gibbs states remains a topic of contention. We use the knowledge of work statistics developed in nonequilibrium thermodynamics to study this problem. Consequently, we deduce a universal theorem delineating the characteristics of evolutions that transition an initial Gibbs state to another. Based on this theorem, we analytically ascertain that adiabatic evolutions fail to transition a non-interacting Gibbs state to its interacting counterpart. However, this adiabatic approach remains a superior approximation relative to its non-adiabatic counterpart. Numerics verifying our theory and predictions are also provided. Furthermore, our findings render insights into the preparation of Gibbs states within the domain of quantum computation.