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Updated: May 8, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Matrix-valued Boltzmann equation for the nonintegrable Hubbard chain.
Martin L R Fürst1, Christian B Mendl, Herbert Spohn
1Excellence Cluster Universe, Technische Universität München, Boltzmannstrasse 2, 85748 Garching bei München, Germany. mfuerst@ma.tum.de
Summary
Adding longer range hopping to the Fermi-Hubbard chain restores thermalization. Systems rapidly approach equilibrium, though intermediate quasistationary states appear with small next-nearest neighbor interactions.
Area of Science:
- Condensed Matter Physics
- Quantum Dynamics
- Statistical Mechanics
Background:
- The standard Fermi-Hubbard chain exhibits complex dynamics.
- Integrability and thermalization are key concepts in many-body physics.
Purpose of the Study:
- To investigate the impact of longer range hopping on the Fermi-Hubbard chain.
- To understand the conditions for thermalization in nonintegrable quantum systems.
Main Methods:
- Numerical investigation of the Fermi-Hubbard chain dynamics.
- Analysis using a Boltzmann-type kinetic equation for the spatially homogeneous case.
Main Results:
- Nonintegrability is introduced by longer range hopping amplitudes.
- The degeneracy of stationary states is lost, restoring convergence to the Fermi-Dirac distribution.
- Exponentially fast convergence to equilibrium is observed, with rapid initial relaxation to quasistationary states for small next-nearest neighbor hopping.
Conclusions:
- Longer range hopping in the Fermi-Hubbard chain drives the system towards thermalization.
- The presence of quasistationary states indicates a two-stage relaxation process.
- Understanding these dynamics is crucial for quantum simulation and condensed matter theory.
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