English

Dissipative systems fractionally coupled to a bath

Statistical Mechanics 2024-06-05 v1

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.

Keywords

Cite

@article{arxiv.2307.10795,
  title  = {Dissipative systems fractionally coupled to a bath},
  author = {Audrique Vertessen and Robin C. Verstraten and Cristiane Morais Smith},
  journal= {arXiv preprint arXiv:2307.10795},
  year   = {2024}
}

Comments

16 pages, 4 figures

R2 v1 2026-06-28T11:35:48.779Z