Non-Markovianity of Quantum Brownian Motion

TL;DR

This paper investigates quantum non-Markovian dynamics in the Caldeira-Leggett model of quantum Brownian motion, analyzing memory effects across various parameters using an exact solution and the Bures metric.

Contribution

It provides a comprehensive analysis of quantum memory effects in the Caldeira-Leggett model using an exact solution and introduces a method to quantify non-Markovianity with the Bures metric.

Findings

Memory effects vary with coupling strength, temperature, and cutoff frequency.

Quantum non-Markovianity shows structural similarities between the Caldeira-Leggett and spin-boson models.

The approach applies to arbitrary Gaussian initial states across dissipation regimes.

Abstract

We study quantum non-Markovian dynamics of the Caldeira-Leggett model, a prototypical model for quantum Brownian motion describing a harmonic oscillator linearly coupled to a reservoir of harmonic oscillators. Employing the exact analytical solution of this model one can determine the size of memory effects for arbitrary couplings, temperatures and frequency cutoffs. Here, quantum non-Markovianity is defined in terms of the flow of information between the open system and its environment, which is quantified through the Bures metric as distance measure for quantum states. This approach allows us to discuss quantum memory effects in the whole range from weak to strong dissipation for arbitrary Gaussian initial states. A comparison of our results with the corresponding results for the spin-boson problem show a remarkable similarity in the structure of non-Markovian behavior of the two paradigmatic models.