Dissipative systems fractionally coupled to a bath
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866929372184707072 |
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| author | Vertessen, Audrique Verstraten, Robin C. Smith, Cristiane Morais |
| author_facet | Vertessen, Audrique Verstraten, Robin C. Smith, Cristiane Morais |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_10795 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dissipative systems fractionally coupled to a bath Vertessen, Audrique Verstraten, Robin C. Smith, Cristiane Morais Statistical Mechanics 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. |
| title | Dissipative systems fractionally coupled to a bath |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2307.10795 |