Engineering quasi-steady-state correlations in uncorrelated thermal states using stochastic driving

TL;DR

This paper introduces a method to engineer specific steady-state correlation functions in quantum systems using stochastic driving, enabling the creation of power-law correlations in fermionic Green's functions.

Contribution

The authors develop a reverse engineering scheme for Markov processes to generate desired steady-state correlations in quantum systems, extending to four-point functions.

Findings

Power-law correlated fermionic Green's functions can be generated at short times.

Disorder in two-point correlations disappears at the quasi-steady state.

Density-density correlations maintain power-law trends despite steady-state disorder.

Abstract

Nonequilibrium quantum dynamics can give rise to the emergence of novel steady states. We propose a scheme for driving an initially uncorrelated thermal state to generate customized correlation functions by determining and reverse engineering the steady-state two-point functions for a class of Markov processes. We also extend the formalism to the calculation of four-point functions. We then apply our method to generating power-law correlated fermionic Green's functions. Furthermore, we find that the power-law patterns emerge at much shorter times than the convergence to the steady state, at which point the disorder in the two-point correlations disappears. On the other hand, the density-density correlations exhibit steady-state disorder while following a power-law trendline. These ideal steady states appear as intermediate-time quasi-steady states in the presence of perturbations.