Open quantum-classical systems: A hybrid MASH master equation

TL;DR

This paper introduces a hybrid quantum-classical method combining surface hopping with Lindblad dynamics, enabling efficient simulation of open quantum systems with classical and quantum interactions.

Contribution

It develops a novel approach integrating MASH with Lindblad equations using stochastic trajectories, extending surface hopping to open quantum systems.

Findings

Accurately models open quantum systems with classical and quantum baths.

Shows excellent agreement with fully quantum benchmarks on spin-boson and molecular fluorescence.

Enables simulation of non-Markovian classical and Markovian quantum environments.

Abstract

We propose a method which combines the quantum-classical mapping approach to surface hopping (MASH) with the dissipative quantum dynamics of the Lindblad master equation. Like conventional surface-hopping methods, our approach is based on classical trajectories coupled to the dynamics of a quantum subsystem. However, instead of evolving the subsystem wavefunction according to the time-dependent Schr\"odinger equation, we use stochastic quantum trajectories derived from secular Redfield theory. This enables the simulation of open quantum systems coupled simultaneously to Markovian quantum baths and anharmonic non-Markovian classical degrees of freedom. Applications to the spin--boson model and to the cavity-enhanced fluorescence of an electronically nonadiabatic molecule show excellent agreement with fully quantum-mechanical benchmarks.