A numerical method for generation of quantum noise and solution of generalized c-number quantum Langevin equation

TL;DR

This paper introduces a numerical method to generate quantum noise with arbitrary correlations and solve the generalized quantum Langevin equation, enabling detailed analysis of quantum Brownian motion and related phenomena.

Contribution

It extends previous theoretical work to develop a practical numerical scheme for quantum noise generation and Langevin equation solutions at any temperature.

Findings

Demonstrates quantum Kramers turnover in mean first passage time

Shows quantum Arrhenius behavior in potential escape rates

Validates the method with numerical simulations

Abstract

Based on a coherent state representation of noise operator and an ensemble averaging procedure we have recently developed [Phys. Rev. E {\bf 65}, 021109 (2002); {\it ibid.} 051106 (2002)] a scheme for quantum Brownian motion to derive the equations for time evolution of {\it true} probability distribution functions in $c$-number phase space. We extend the treatment to develop a numerical method for generation of $c$-number noise with arbitrary correlation and strength at any temperature, along with the solution of the associated generalized quantum Langevin equation. The method is illustrated with the help of a calculation of quantum mean first passage time in a cubic potential to demonstrate quantum Kramers turnover and quantum Arrhenius plot.