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.
