The Phase-Coupled Caldeira-Leggett Model: Non-Markovian Open Quantum Dynamics beyond Linear Dissipation

TL;DR

This paper introduces the Phase-Coupled Caldeira-Leggett model, a non-Markovian quantum dissipation framework with exponential system-bath coupling, unifying quantum Brownian motion and polaron physics, and providing exact dynamics beyond linear response.

Contribution

The paper develops an exact, nonperturbative framework for a novel nonlinear quantum dissipation model with exponential system-bath coupling, extending beyond traditional linear models.

Findings

Exact equation of motion for the reduced density operator.

Distinct dynamical behaviors compared to linear Caldeira-Leggett model.

Nonperturbative treatment enabled by Gaussian environment.

Abstract

We introduce the \textit{Phase-Coupled Caldeira-Leggett} (PCL) model of quantum dissipation and develop an exact framework for its dynamics. Unlike the conventional Caldeira-Leggett model with linear system-bath coupling $H_{\mathrm{SB}}\propto\hat F$, the PCL model features an exponential interaction $H_{\mathrm{SB}}\propto e^{i\lambda \hat F}$, where $\hat F$ denotes the collective bath coordinate. This model unifies concepts from quantum Brownian motion and polaron physics, providing a general platform to study phase-mediated dissipation and decoherence beyond the linear-response regime. Despite its nonlinear system-bath coupling, the Gaussian nature of the environment allows a nonperturbative and non-Markovian treatment of PCL model within the algebra of dissipative quasiparticles. We obtain an exact closed-form equation of motion for the reduced density operator, and numerical simulations reveal distinctive dynamical behaviors that deviate markedly from those predicted by the conventional Caldeira-Leggett model.