Dynamics of isolated quantum many-body systems far from equilibrium

by Markus Schmitt
Doctoral thesis
Date of Examination:2018-01-11
Date of issue:2018-01-22
Advisor:Prof. Dr. Stefan Kehrein
Referee:Prof. Dr. Stefan Kehrein
Referee:Prof. Dr. Reiner Kree
Referee:Prof. Dr. Martin Eckstein
Persistent Address: http://dx.doi.org/10.53846/goediss-6693

 

 

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Abstract

English

This thesis addresses different aspects of the dynamics of isolated quantum many-body systems far from equilibrium, ranging from transient phenomena at short times to questions about relaxation and equilibration at late times. The first part deals with nonequilibrium critical phenomena. Dynamical quantum phase transitions are characterized in a two-dimensional spin system by studying the distribution of Fisher zeros in the complex time plane. Moreover, a new topologically driven transition in the nonequilibrium steady state of quenched Chern insulators is investigated, resulting in the identification of universal nonanalytic behavior of the Hall conductance as a function of the quench parameter. The second part of the thesis comprises a study of transient dynamics of the transverse-field Ising model in two and three dimensions based on a perturbative derivation of classical networks to encode the time-evolved wave function; this construction is also applicable to represent the state as an artificial neural network. In the last part of the thesis a possible definition of the irreversibility of quantum many-body dynamics is introduced, which is based on the echo dynamics of observables under imperfect effective time reversal. Echo dynamics is studied in generic and integrable quantum systems as well as in the semiclassical limit. The relation to out-of-time-order correlators is explored, which were recently introduced to probe the quantum butterfly effect.
Keywords: Quantum many-body dynamics; Nonequilibrium dynamics; Quantum many-body theory; Quench dynamics; Dynamical quantum phase transitions; Nonequilibrium phase transitions; Quantum dynamics from classical networks; Artificial neural network wave functions; Irreversibility; Quantum chaos; Echo dynamics; Effective time reversal; Quantum butterfly effect; Out-of-time-order
 
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