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arXiv · 2307.10795

Dissipative systems fractionally coupled to a bath

Audrique Vertessen·Robin C. Verstraten·Cristiane Morais Smith
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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.

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Audrique Vertessen, Robin C. Verstraten, Cristiane Morais Smith. 2023-07-20. Dissipative systems fractionally coupled to a bath. https://doi.org/10.1063/5.0204304

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