# Modelling a Bistable System Strongly Coupled to a Debye Bath: A Quasiclassical Approach Based on the Generalised Langevin Equation

## TL;DR

This paper extends the Generalised Langevin Equation (GLE) to model quantum fluctuations in a strongly coupled bistable system, capturing key quantum effects and transition rate behaviors with a quasiclassical approach.

## Contribution

The authors develop a quasiclassical GLE method that incorporates quantum fluctuations, enabling more accurate modeling of transition rates in strongly coupled bistable systems.

## Key findings

- Isotopic effects observed in transition rates.
- Quantum and classical rates converge at strong coupling.
- Saturation of rates at low temperature qualitatively matches predictions.

## Abstract

Bistable systems present two degenerate metastable configurations separated by an energy barrier. Thermal or quantum fluctuations can promote the transition between the configurations at a rate which depends on the dynamical properties of the local environment (i.e., a thermal bath). In the case of classical systems, strong system-bath interaction has been successfully modelled by the Generalised Langevin Equation (GLE) formalism. Here we show that the efficient GLE algorithm introduced in Phys. Rev. B 89, 134303 (2014) can be extended to include some crucial aspects of the quantum fluctuations. In particular, the expected isotopic effect is observed along with the convergence of the quantum and classical transition rates in the strong coupling limit. Saturation of the transition rates at low temperature is also retrieved, in qualitative, yet not quantitative, agreement with the analytic predictions. The discrepancies in the tunnelling regime are due to an incorrect sampling close to the barrier top. The domain of applicability of the quasiclassical GLE is also discussed.