Dissipative systems fractionally coupled to a bath

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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 Liouville fractional derivative. The Liouville fractional Langevin equation is then derived in the classical regime, without imposing a non-Ohmic macroscopic spectral function for the bath. By investigating the short- and long-time behavior of the mean squared displacement, 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.
Original languageEnglish
Article number063103
Pages (from-to)1-15
Number of pages15
Issue number6
Publication statusPublished - Jun 2024


  • Anomalous diffusion
  • Dynamics
  • Langevin equation
  • Particles
  • Quantum diffusion
  • Random-walks


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