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Title
Quench dynamics in quantum integrable models of many body systems
Lecturer
Professor Natan Andrei(Rutgers University)
Date and time
Jul,4,2014, 16:00-
Place
H345, Main Building, O-Okayama Campus, Tokyo Institute of Technology.
Abstract
I will describe a formulation for studying the quench dynamics of integrable systems generalizing an approach by Yudson. I'll discuss the evolution Lieb-Liniger system, a gas of interacting bosons moving on the continuous infinite line and interacting via a short range potential. The formalism allows us to quench the system from any initial state. Considering first a finite number of bosons on the line we find that for any value of repulsive coupling the system asymptotes towards a strongly repulsive gas for any initial state, while for an attractive coupling, the system forms a maximal bound state that dominates at longer times. In either case the system equilibrates but does not thermalize, an effect that is consistent with prethermalization. Then considering the system in the thermodynamic limit - with the number of bosons and the system size sent to infinity at a constant density with the long time limit taken subsequently- I'll discuss the equilibration of the density and density-density correlation functions for strong but finite positive coupling and show they are described by GGE (generalized Gibbs ensemble) for translationally invariant initial states with short range correlations. For initial states with long range correlations a generalized GGE emerges. If the initial state is strongly non translationally invariant the system does not equilibrate. I will give some example of quenches: from a Mott insulator initial state or a domain wall configuration. Then I will show that if the coupling constant is negative the GGE fails for most initial states.
If time permits I shall discuss also the quench dynamics of the XXZ Heisenberg chain and of a mobile impurity in an interacting Bose gas.
Contact
Prof. Tomohiro Sasamoto(2736)