Dissipative systems fractionally coupled to a bath

TL;DR

This paper generalizes the Caldeira-Leggett model by coupling a bath to a system via a Weyl fractional derivative, enabling the description of various anomalous diffusion behaviors in quantum systems.

Contribution

It introduces a fractional derivative coupling in the model, deriving a Weyl fractional Langevin equation without relying on a non-Ohmic spectral function.

Findings

The model captures ballistic, sub-ballistic, and super-ballistic short-time diffusion.

It predicts saturation, sub-diffusion, and super-diffusion at long times.

The approach broadens the understanding of quantum diffusion phenomena.

Abstract

Quantum diffusion is a major topic in condensed-matter physics, and the Caldeira-Leggett model has been one of the most successful approaches to study this phenomenon. Here, we generalize this model by coupling the bath to the system through a Weyl fractional derivative. The Weyl fractional Langevin equation is then derived without imposing a non-Ohmic macroscopic spectral function for the bath. By investigating the short- and long-time behavior of the mean squared displacement (MSD), we show that this model is able to describe a large variety of anomalous diffusion. Indeed, we find ballistic, sub-ballistic, and super-ballistic behavior for short times, whereas for long times we find saturation, and sub- and super-diffusion.