A Stochastic Liouvillian Algorithm to Simulate Dissipative Quantum Dynamics With Arbitrary Precision

TL;DR

This paper introduces an exact stochastic Liouville equation-based algorithm for simulating dissipative quantum dynamics with arbitrary precision, applicable to systems at any temperature and dissipation level.

Contribution

The paper presents a novel stochastic Liouville algorithm derived from path-integral formalism, enabling precise simulation of dissipative quantum systems across all regimes.

Findings

Successfully applied to a damped harmonic oscillator.

Accurately modeled a double-well system in an Ohmic bath.

Demonstrated effectiveness at low temperatures.

Abstract

An exact and efficient new method to simulate dynamics in dissipative quantum systems is presented. A stochastic Liouville equation, deduced from Feynman and Vernon's path-integral expression of the reduced density matrix, is used to describe the exact dynamics at any dissipative strength and for arbitrarily low temperatures. The utility of the method is demonstrated by applications to a damped harmonic oscillator and a double-well system immersed in an Ohmic bath at low temperatures.