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Dissipative systems fractionally coupled to a bath.

A Vertessen¹, R C Verstraten¹, C Morais Smith¹

¹Institute for Theoretical Physics, Utrecht University, Princetonplein 5, 3584CC Utrecht, The Netherlands.

Chaos (Woodbury, N.Y.)

|June 3, 2024

Summary

This study generalizes the Caldeira-Leggett model for quantum diffusion using a Liouville fractional derivative, revealing diverse anomalous diffusion behaviors in condensed-matter physics.

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Experimental Multiscale Methodology for Predicting Material Fouling Resistance

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Area of Science:

Condensed-matter physics
Quantum mechanics
Statistical mechanics

Background:

The Caldeira-Leggett model is a cornerstone for studying quantum diffusion.
Understanding anomalous diffusion is crucial in various physical systems.

Purpose of the Study:

To generalize the Caldeira-Leggett model for quantum diffusion.
To investigate anomalous diffusion phenomena using a novel theoretical framework.

Main Methods:

Coupling the bath to the system via a Liouville fractional derivative.
Deriving the Liouville fractional Langevin equation in the classical regime.
Analyzing the short- and long-time behavior of mean squared displacement.

Main Results:

The generalized model describes a wide range of anomalous diffusion.
Ballistic, sub-ballistic, and super-ballistic behaviors observed at short times.
Saturation, sub-diffusion, and super-diffusion observed at long times.

Conclusions:

The Liouville fractional derivative approach offers a versatile framework for quantum diffusion.
This model successfully captures diverse anomalous diffusion regimes without spectral function constraints.
The findings contribute to a deeper understanding of quantum transport phenomena.