Quantum dissipation with nonlinear environment couplings: Stochastic fields dressed dissipaton equation of motion approach

TL;DR

This paper introduces a stochastic-fields-dressed dissipaton equation of motion (SFD-DEOM) method that efficiently simulates quantum dissipation with nonlinear environment couplings by transforming the problem into a linear coupling framework using stochastic fields.

Contribution

The paper develops an exact, nonperturbative SFD-DEOM approach that simplifies nonlinear environment couplings into linear ones via stochastic fields, enhancing simulation efficiency and stability.

Findings

Successfully applied to a two-state model system.

Demonstrates high efficiency and stability in simulations.

Provides an exact approach for nonlinear quantum dissipation.

Abstract

Accurate and efficient simulation on quantum dissipation with nonlinear environment couplings remains nowadays a challenging task. In this work, we propose to incorporate the stochastic fields, which resolve just the nonlinear environment coupling terms, into the dissipaton-equation-of-motion (DEOM) construction. The stochastic fields are introduced via the Hubbard-Stratonovich transformation. After the transformation, the resulted stochastic-fields-dressed total Hamiltonian contains only linear environment coupling terms. On basis of that, a stochastic-fields-dressed DEOM (SFD-DEOM) can then be constructed. The resultant SFD-DEOM, together with the ensemble average over the stochastic fields, constitutes an exact and nonperturbative approach to quantum dissipation under nonlinear environment couplings. It is also of relatively high efficiency and stability due to the fact that only nonlinear environment coupling terms are dealt with stochastic fields while linear couplings are still treated as the usual DEOM. Numerical demonstrations are carried out on a two-state model system.