Thermalization in one-dimensional quantum-many-body systems

by Fabian Ralf Anton Biebl
Doctoral thesis
Date of Examination:2016-12-14
Date of issue:2017-01-16
Advisor:Prof. Dr. Stefan Kehrein
Referee:Prof. Dr. Stefan Kehrein
Referee:Prof. Dr. Peter E. Blöchl
Referee:Prof. Dr. Reiner Kree
Referee:PD Dr. Salvatore R. Manmana
Referee:Prof. Dr. Stefan Mathias
Referee:Prof. Dr. Cynthia A. Volkert
Persistent Address: http://dx.doi.org/10.53846/goediss-6079

 

 

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Abstract

English

We consider the thermalization of the momentum distribution in two one-dimensional models. The first one is the integrable Hubbard model with an additional integrability breaking term in the Hamiltonian, which is a next-to-nearest-neighbor hopping term. This has been previously investigated by Fürst et al. (PRE 86:031122, 2012; PRE 88:012108, 2013). They considered several initial quasiparticle momentum distributions and their relaxation times for different strengths of the next-to-nearest-neighbor hopping amplitude. We find the dependence of the thermalization rates on the model parameters, on the filling and on temperature for any initial quasiparticle momentum distribution in the regime of small integrability breaking using a Boltzmann equation. The second model is an effective model describing a chain of manganite octahedra. There, we investigate a the temperature dependence of the relaxation rates for reasonable choices of the model parameters and the filling.
Keywords: thermalization; Boltzmann equation; Hubbard model; non-equilibrium; condensed matter; electrons; manganites
 
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