Analyzing and predicting non-equilibrium many-body dynamics via dynamic mode decomposition

TL;DR

This paper explores using dynamic mode decomposition (DMD), a data-driven technique, to efficiently predict long-term nonequilibrium quantum many-body dynamics from limited short-time data, demonstrating its effectiveness and addressing potential pitfalls.

Contribution

The paper introduces the application of DMD to predict nonequilibrium quantum dynamics, showing its advantages over traditional Fourier extrapolation and addressing resolution issues with higher order DMD.

Findings

DMD accurately predicts long-term dynamics from short-time data.

DMD results are consistent with linear response analysis in equilibrium.

Higher order DMD overcomes discretization resolution issues.

Abstract

Simulating the dynamics of a nonequilibrium quantum many-body system by computing the two-time Green's function associated with such a system is computationally challenging. However, we are often interested in the time diagonal of such a Green's function or time dependent physical observables that are functions of one time. In this paper, we discuss the possibility of using dynamic model decomposition (DMD), a data-driven model order reduction technique, to characterize one-time observables associated with the nonequilibrium dynamics using snapshots computed within a small time window. The DMD method allows us to efficiently predict long time dynamics from a limited number of trajectory samples. We demonstrate the effectiveness of DMD on a model two-band system. We show that, in the equilibrium limit, the DMD analysis yields results that are consistent with those produced from a linear response analysis. In the nonequilibrium case, the extrapolated dynamics produced by DMD is more accurate than a special Fourier extrapolation scheme presented in this paper. We point out a potential pitfall of the standard DMD method caused by insufficient spatial/momentum resolution of the discretization scheme. We show how this problem can be overcome by using a variant of the DMD method known as higher order DMD.