2 research outputs found
Free expansion of a Lieb-Liniger gas: Asymptotic form of the wave functions
The asymptotic form of the wave functions describing a freely expanding
Lieb-Liniger gas is derived by using a Fermi-Bose transformation for
time-dependent states, and the stationary phase approximation. We find that
asymptotically the wave functions approach the Tonks-Girardeau (TG) structure
as they vanish when any two of the particle coordinates coincide. We point out
that the properties of these asymptotic states can significantly differ from
the properties of a TG gas in a ground state of an external potential. The
dependence of the asymptotic wave function on the initial state is discussed.
The analysis encompasses a large class of initial conditions, including the
ground states of a Lieb-Liniger gas in physically realistic external
potentials. It is also demonstrated that the interaction energy asymptotically
decays as a universal power law with time, .Comment: Section VI added to v2; published versio
2PI nonequilibrium versus transport equations for an ultracold Bose gas
The far-from-equilibrium dynamics of an ultracold, one-dimensional Bose gas
is studied. The focus is set on the comparison between the solutions of fully
dynamical evolution equations derived from the 2PI effective action and their
corresponding kinetic approximation in the form of Boltzmann-type transport
equations. It is shown that during the time evolution of the gas a kinetic
description which includes non-Markovian memory effects in a gradient expansion
becomes valid. The time scale at which this occurs is shown to exceed
significantly the time scale at which the system's evolution enters a
near-equilibrium drift period where a fluctuation dissipation relation is found
to hold and which would seem to be predestined for the kinetic approximation.Comment: 24 pages, 7 figures. References adde