### Abstract

Weakly interacting quantum fluids allow for a natural kinetic theory description which takes into account the fermionic or bosonic nature of the interacting particles. In the simplest cases, one arrives at the Boltzmann–Nordheim equations for the reduced density matrix of the fluid. We discuss here two related topics: the kinetic theory of the fermionic Hubbard model, in which conservation of total spin results in an additional Vlasov-type term in the Boltzmann equation, and the relation between kinetic theory and thermalization. © Springer Nature Switzerland AG 2018.

Original language | English |
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Title of host publication | Macroscopic Limits of Quantum Systems : Munich, Germany, March 30 - April 1, 2017 |

Editors | Daniela Cadamuro, Maximilian Duell, Wojciech Dybalski, Sergio Simonella |

Number of pages | 28 |

Place of Publication | Cham |

Publisher | Springer |

Publication date | 2018 |

Pages | 1-28 |

ISBN (Print) | 978-3-030-01601-2 |

ISBN (Electronic) | 978-3-030-01602-9 |

DOIs | |

Publication status | Published - 2018 |

MoE publication type | A4 Article in conference proceedings |

Event | Macroscopic Limits of Quantum Systems - Technische Universität München, Munich, Germany Duration: 30 Mar 2017 → 1 Apr 2017 https://www-m5.ma.tum.de/Allgemeines/MacroscopicLimitsWorkshop |

### Publication series

Name | Springer Proceedings in Mathematics and Statistics |
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Volume | 270 |

ISSN (Print) | 2194-1009 |

ISSN (Electronic) | 2194-1017 |

### Fields of Science

- Boltzmann equation
- Kinetics
- Quantum chemistry
- Quantum optics
- Vlasov equation, Boltzmann
- Interacting fermions
- Interacting particles
- Quantum fluids
- Reduced-density matrix
- Thermalization, Kinetic theory
- 111 Mathematics

## Cite this

Lukkarinen, J. (2018). Kinetic theory and thermalization of weakly interacting fermions. In D. Cadamuro, M. Duell, W. Dybalski, & S. Simonella (Eds.),

*Macroscopic Limits of Quantum Systems : Munich, Germany, March 30 - April 1, 2017*(pp. 1-28). (Springer Proceedings in Mathematics and Statistics; Vol. 270). Cham: Springer. https://doi.org/10.1007/978-3-030-01602-9_1