Quantum-Classical Liouville Dynamics in the Mapping Basis

TL;DR

This paper derives a new representation of the quantum-classical Liouville equation in the mapping basis, enabling nonadiabatic dynamics calculations without surface-hopping, and demonstrates its accuracy on the spin-boson model.

Contribution

It introduces a mapping basis formulation of the quantum-classical Liouville equation, providing an alternative to surface-hopping methods for simulating quantum dynamics.

Findings

Close agreement with exact quantum results for the spin-boson system

Provides a new computational route for nonadiabatic dynamics

Exact for the spin-boson model in the derived form

Abstract

The quantum-classical Liouville equation describes the dynamics of a quantum subsystem coupled to a classical environment. It has been simulated using various methods, notably, surface-hopping schemes. A representation of this equation in the mapping Hamiltonian basis for the quantum subsystem is derived. The resulting equation of motion, in conjunction with expressions for quantum expectation values in the mapping basis, provide another route to the computation of the nonadiabatic dynamics of observables that does not involve surface-hopping dynamics. The quantum-classical Liouville equation is exact for the spin-boson system. This well-known model is simulated using an approximation to the evolution equation in the mapping basis and close agreement with exact quantum results is found.