# Coherent State Mapping Ring-Polymer Molecular Dynamics for Non-Adiabatic quantum propagations

## TL;DR

The paper presents CS-RPMD, a novel method combining coherent state mapping and ring-polymer techniques to accurately simulate non-adiabatic quantum dynamics with explicit nuclear quantization, preserving key quantum features.

## Contribution

Introduces CS-RPMD, a new approach that accurately models electronic non-adiabatic dynamics with explicit nuclear quantization, ensuring correct Rabi oscillations and detailed balance.

## Key findings

- Accurately reproduces quantum results for a two-state model.
- Preserves detailed balance in the one-bead limit.
- Shows good agreement with exact quantum dynamics across various couplings.

## Abstract

We introduce the coherent state mapping ring-polymer molecular dynamics (CS-RPMD), a new method that accurately describes electronic non-adiabatic dynamics with explicit nuclear quantization. This new approach is derived by using coherent state mapping representation for the electronic degrees of freedom (DOF) and the ring-polymer path-integral representation for the nuclear DOF. CS-RPMD Hamiltonian does not contain any inter-bead coupling term in the state-dependent potential, which is a key feature that ensures correct electronic Rabi oscillations. Hamilton's equation of motion is used to sample initial configurations and propagate the trajectories, preserving the distribution with classical symplectic evolution. In the special one-bead limit for mapping variables, CS-RPMD preserves the detailed balance. Numerical tests of this method with a two-state model system show a very good agreement with exact quantum results over a broad range of electronic couplings.