Non- Markovian Quantum Stochastic Equation For Two Coupled Oscillators

TL;DR

This paper derives a non-Markovian quantum stochastic equation for two coupled oscillators interacting with a heat bath, providing analytical expressions for transport coefficients and fluctuation-dissipation relations in nonlinear quantum systems.

Contribution

It introduces a novel non-Markovian quantum stochastic framework for coupled oscillators, including explicit formulas for time-dependent friction and diffusion coefficients.

Findings

Explicit expressions for transport coefficients are obtained.

Generalized Langevin equations are derived for nonlinear non-Markovian noise.

Fluctuation-dissipation relations are established for the system.

Abstract

The system of nonlinear Langevin equations was obtained by using Hamiltonian's operator of two coupling quantum oscillators which are interacting with heat bath. By using the analytical solution of these equations, the analytical expressions for transport coefficients was found. Generalized Langevin equations and fluctuation-dissipation relations are derived for the case of a nonlinear non-Markovian noise. The explicit expressions for the time-dependent friction and diffusion coefficients are presented for the case of linear couplings in the coordinate between the collective two coupled harmonic oscillators and heat bath.