Quantum Langevin approach for non-Markovian quantum dynamics of the spin-boson model

TL;DR

This paper introduces a non-Markovian quantum Langevin approach to solve the spin-boson model, enabling more efficient numerical simulations of quantum dissipative dynamics in non-Markovian regimes.

Contribution

The authors develop a novel non-Markovian quantum Langevin method that derives noise-free quantum Bloch equations for the spin-boson model, improving upon existing stochastic approaches.

Findings

Derivation of non-Markovian quantum Bloch equations without explicit noise variables

Enhanced numerical simulation efficiency for non-Markovian quantum dynamics

Broader applicability to quantum noise control and open system theories

Abstract

One long-standing difficult problem in quantum dissipative dynamics is to solve the spin-boson model in a non-Markovian regime where a tractable systematic master equation does not exist. The spin-boson model is particularly important due to its crucial applications in quantum noise control and manipulation as well as its central role in developing quantum theories of open systems. Here we solve this important model by developing a non-Markovian quantum Langevin approach. By projecting the quantum Langevin equation onto the coherent states of the bath, we can derivie a set of non-Markovian quantum Bloch equations containing no explicit noise variables. This special feature offers a tremendous advantage over the existing stochastic Schr\"odinger equations in numerical simulations. The physical significance and generality of our approach are briefly discussed.