# Dissipation in the Caldeira-Leggett model

## TL;DR

This paper reexamines the Caldeira-Leggett model, revealing that its master equation is inherently non-Markovian and non-dissipative, challenging previous assumptions about its Markovian nature and the origin of dissipation.

## Contribution

The study demonstrates that the Caldeira-Leggett model's master equation is non-dissipative and inherently non-Markovian, providing a new understanding of quantum Brownian motion.

## Key findings

- The original CL master equation is non-dissipative upon careful analysis.
- Dissipation in quantum Brownian motion arises from non-Markovian effects.
- A microscopic description requires non-Markovian dynamics.

## Abstract

Caldeira and Leggett (CL) in a seminal paper derived a master equation describing Markovian Quantum Brownian motion. Such an equation suffered of not being completely positive, and many efforts have been made to solve this issue. We show that, when a careful mathematical analysis is performed, the model considered by CL leads to a non dissipative master equation. We argue that the correct way to understand the master equation derived in the CL regime is to consider it non-Markovian. Moreover, we show that if one wants to provide a microscopic description of Quantum Brownian motion with the CL model, one always needs to consider a non-Markovian dynamics. We conclude that dissipation is a genuinely non-Markovian feature.