A Langevin canonical approach to the dynamics of two level systems. I. Populations and coherences

TL;DR

This paper develops a canonical framework to analyze the dynamics of chiral two-level systems coupled to a harmonic oscillator bath, focusing on populations and coherences, and explores regimes of tunneling with numerical and analytical methods.

Contribution

It introduces a stochastic canonical approach to derive equilibrium populations and coherences, extending beyond the non-interacting blip approximation for two-level systems.

Findings

Identifies critical temperature for tunneling regimes.

Provides numerical solutions fitted with analytical expressions.

Analyzes incoherent and coherent tunneling regimes.

Abstract

A canonical framework for chiral two--level systems coupled to a bath of harmonic oscillators is developed to extract, from a stochastic dynamics, the thermodynamic equilibrium values of both the population difference and coherences. The incoherent and coherent tunneling regimes are analyzed for an Ohmic environment in terms of a critical temperature defined by the maximum of the heat capacity. The corresponding numerical results issued from solving a non-linear coupled system are fitted to approximate path--integral analytical expressions beyond the so-called non-interacting blip approximation in order to determine the different time scales governing both regimes.