Solving Caldeira-Leggett Model by Inchworm Method with Frozen Gaussian Approximation

TL;DR

This paper introduces a novel algorithm combining the inchworm method and frozen Gaussian approximation to efficiently simulate the real-time dynamics of the Caldeira-Leggett model, capturing quantum particle interactions with thermal baths.

Contribution

The paper presents a new computational approach that integrates the inchworm method with frozen Gaussian approximation for improved simulation of open quantum systems.

Findings

Efficient simulation of the Caldeira-Leggett model demonstrated.

Faster convergence of Dyson series achieved.

Accurate real-time dynamics captured in numerical experiments.

Abstract

We propose an algorithm that combines the inchworm method and the frozen Gaussian approximation to simulate the Caldeira-Leggett model in which a quantum particle is coupled with thermal harmonic baths. In particular, we are interested in the real-time dynamics of the reduced density operator. In our algorithm, we use frozen Gaussian approximation to approximate the wave function as a wave packet in integral form. The desired reduced density operator is then written as a Dyson series, which is the series expression of path integrals in quantum mechanics of interacting systems. To compute the Dyson series, we further approximate each term in the series using Gaussian wave packets, and then employ the idea of the inchworm method to accelerate the convergence of the series. The inchworm method formulates the series as an integro-differential equation of ``full propagators'', and rewrites the infinite series on the right-hand side using these full propagators, so that the number of terms in the sum can be significantly reduced, and faster convergence can be achieved. The performance of our algorithm is verified numerically by various experiments.