Differential Equation Based Path Integral for System-Bath Dynamics

TL;DR

The paper introduces a differential equation based path integral method for simulating open quantum system dynamics, reducing memory costs compared to existing techniques through novel numerical schemes.

Contribution

It develops a new DEBPI approach derived from i-QuAPI, with a closure scheme to create finite systems and improve computational efficiency.

Findings

Memory cost can be significantly reduced in certain cases.

New numerical schemes derived from differential equations improve simulation efficiency.

Method verified through numerical experiments.

Abstract

We propose the differential equation based path integral (DEBPI) method to simulate the real-time evolution of open quantum systems. In this method, a system of partial differential equations is derived based on the continuation of a classical numerical method called iterative quasi-adiabatic propagator path integral (i-QuAPI). While the resulting system has infinite equations, we introduce a reasonable closure to obtain a series of finite systems. New numerical schemes can be derived by discretizing these differential equations. It is numerically verified that in certain cases, by selecting appropriate systems and applying suitable numerical schemes, the memory cost required in the i-QuAPI method can be significantly reduced.