Lecturer: Prof. Natan Andrei
Affiliation: Department of Physics and Astronomy,
Rutgers, The State University of New Jersey
Abstract:
I will describe nonequilibrium dynamics
in interacting quantum systems, mainly
using the protocol of quenching the
systems and following their evolution in
time. I'll discuss the evolution of the Lieb-
Liniger system, a gas of interacting
bosons moving on the continuous infinite
line and interacting via a short range
potential.
Considering first a finite number of
bosons on the line I 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 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. If the initial state
is strongly non translational invariant the
system evolves into a nonequilibrium
steady state (NESS). I will give some
examples of quenches: from a Mott
insulator initial state or from a domain
wall configuration or a Newton’s Cradle.
I also will show that if the coupling
constant is negative the GGE fails for most
initial states in the Lieb-Liniger model. If
time permits I shall discuss the quench
dynamics of the XXZ Heisenberg chain.