Factorization rule for multitime correlations in non-Markovian open quantum systems

TL;DR

This paper introduces an exact factorization rule for multitime correlations in non-Markovian quantum systems with finite memory, enabling efficient calculations where the quantum regression theorem fails.

Contribution

It provides a novel factorization method that relates higher-order multitime correlations to lower-order ones in non-Markovian systems with finite memory times.

Findings

The factorization rule simplifies numerical calculations of multitime correlations.

Demonstrated efficiency in quantum dot-phonon systems.

Enables semi-analytical solutions beyond standard QRT.

Abstract

Experiments performed on quantum systems often measure multitime correlation functions. When quantum systems are weakly coupled to their environment, the time evolution of such correlation functions can be reduced to that of the reduced density matrix by the quantum regression theorem (QRT). While no QRT is available for general non-Markovian open quantum systems, we show that for time-independent Hamiltonians and finite memory times $\tau_c$, an exact factorization rule exists that relates higher-order multitime correlations to products of lower-order correlations. Consequently, all information needed to reconstruct $n$-time correlations is contained in a temporal volume of $\mathcal{O}(\tau_c^n)$. On the example of quantum dots coupled to phonons, we demonstrate that this factorization makes numerical calculations of multitime correlations extremely efficient and even enables semianalytical solutions in systems where the standard QRT breaks down.