Progress towards an effective non-Markovian description of a system interacting with a bath

TL;DR

This paper develops an exact non-Markovian framework for describing a harmonic oscillator coupled to a bath of oscillators, transforming the bath into a chain structure and relating the dynamics to the Generalized Langevin Equation.

Contribution

It introduces a novel chain transformation of the bath and derives exact dynamics, bridging microscopic environmental modes with established non-Markovian models.

Findings

The transformed bath allows exact solution of the system's dynamics.

The derived dynamics satisfy the Generalized Langevin Equation.

The approach provides a new perspective on system-bath interactions.

Abstract

We analyze a system coupled to a bath of independent harmonic oscillators. We transform the bath in chain structure by solving an inverse eigenvalue problem. We solve the equations of motion for the collective variables defined by this transformation, and we derive the exact dynamics for an harmonic oscillator in terms of the microscopic motion of the environmental modes. We compare this approach to the well-known Generalized Langevin Equation and we show that our dynamics satisfies this equation.