18–23 Aug 2014
Nordita, Stockholm
Europe/Stockholm timezone

Quench dynamics in quantum integrable models

22 Aug 2014, 11:30
30m
Oskar Klein-auditoriet (FR4) (Nordita, Stockholm)

Oskar Klein-auditoriet (FR4)

Nordita, Stockholm

Speaker

Prof. Natan Andrei (Rutgers University, USA)

Description

Abstract: I will describe a formulation for studying the quench dynamics of integrable systems generalizing an approach by Yudson  and apply it to the evolution dynamics of the  Lieb-Liniger system, a gas of bosons moving on the continuous 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. I will show 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 system for strong but finite positive coupling and show it equilibrates to a GGE (generalized Gibbs ensemble) for translationally invariant initial states with short  range correlations. For initial states with long range correlations a generalizedGGE emerges. If the initial state is strongly non-translationally invariant the system does not equilibrate.  I will give some examples of quenches: from a Mott insulator initial state or from a domain wall configuration. Then I will show that if the coupling constant is negative the GGE fails for most initial states. The latter result extends to all models with bound states such as the XXZ or the Hubbard model. 
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.

Presentation materials