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Generalized Thermalization in Quantum-Chaotic Quadratic Hamiltonians
Patrycja Łydżba1, Marcin Mierzejewski1, Marcos Rigol2
1Institute of Theoretical Physics, Wroclaw University of Science and Technology, 50-370 Wrocław, Poland.
Abstract:
Thermalization (generalized thermalization) in nonintegrable (integrable) quantum systems requires two ingredients: equilibration and agreement with the predictions of the Gibbs (generalized Gibbs) ensemble. We prove that observables that exhibit eigenstate thermalization in single-particle sector equilibrate in many-body sectors of quantum-chaotic quadratic models. Remarkably, the same observables do not exhibit eigenstate thermalization in many-body sectors (we establish that there are exponentially many outliers). Hence, the generalized Gibbs ensemble is generally needed to describe their expectation values after equilibration, and it is characterized by Lagrange multipliers that are smooth functions of single-particle energies.
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