Journal of Physics A Mathematical and Theoretical

Limits of Born approximation for unequal time correlation functions and detailed balance in open quantum systems

Katha Ganguly, Bijay Kumar Agarwalla

Published Nov 14, 2025• 0 citations

Abstract

Abstract We show that, in general, the unequal time correlation function of system observables, when computed within the Born approximation in open quantum systems, fails to produce the temperature-dependent contributions required for thermalization in the long-time limit. As a consequence, Born approximation fails to respect the detailed balance condition in the long-time limit for arbitrary time difference. This occurs precisely due to the factorization of the total density matrix in the Born approximation, which neglects finite system–bath correlations. We demonstrate how incorporating the correction term recovers the temperature-dependent thermalization term and restores detailed balance. In contrast, we find that so-called spectral correlators, which are unrelated to detailed balance often correctly captured at the Born level to leading order in the system–bath coupling. We also provide a generic condition under which spectral correlators can be correctly predicted under Born approximation. Our approach is illustrated for two paradigmatic models of open quantum systems: (i) the dissipative Caldeira–Leggett model and (ii) the dissipative spin-boson model. We further extend our analysis for multi-bath non-equilibrium quantum transport scenario.

DOI: 10.1088/1751-8121/ae1fc3

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