43 research outputs found
Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
In this Letter we pose the question of whether a many-body quantum system
with a full set of conserved quantities can relax to an equilibrium state, and,
if it can, what the properties of such state are. We confirm the relaxation
hypothesis through a thorough ab initio numerical investigation of the dynamics
of hard-core bosons on a one-dimensional lattice. Further, a natural extension
of the Gibbs ensemble to integrable systems results in a theory that is able to
predict the mean values of physical observables after relaxation. Finally, we
show that our generalized equilibrium carries more memory of the initial
conditions than the usual thermodynamic one. This effect may have many
experimental consequences, some of which having already been observed in the
recent experiment on the non-equilibrium dynamics of one-dimensional hard-core
bosons in a harmonic potential [T. Kinoshita, T. Wenger, D. S. Weiss, Nature
(London) 440, 900 (2006)].Comment: 4 pages, 2 figures, published versio
Memory of the Initial Conditions in an Incompletely-Chaotic Quantum System: Universal Predictions and an Application to Cold Atoms
Two zero-range-interacting atoms in a circular, transversely harmonic
waveguide are used as a test-bench for a quantitative description of the
crossover between integrability and chaos in a quantum system with no selection
rules. For such systems we show that the expectation value after relaxation of
a generic observable is given by a linear interpolation between its initial and
thermal expectation values. The variable of this interpolation is universal; it
governs this simple law to cover the whole spectrum of the chaotic behavior
from integrable regime through the well- developed quantum chaos. The
predictions are confirmed for the waveguide system, where the mode occupations
and the trapping energy were used as the observables of interest; a variety of
the initial states and a full range of the interaction strengths have been
tested.Comment: 4 pages, 2 figure
Dissociation of one-dimensional matter-wave breathers due to quantum many-body effects
We use the ab initio Bethe Ansatz dynamics to predict the dissociation of
one-dimensional cold-atom breathers that are created by a quench from a
fundamental soliton. We find that the dissociation is a robust quantum
many-body effect, while in the mean-field (MF) limit the dissociation is
forbidden by the integrability of the underlying nonlinear Schr\"{o}dinger
equation. The analysis demonstrates the possibility to observe quantum
many-body effects without leaving the MF range of experimental parameters. We
find that the dissociation time is of the order of a few seconds for a typical
atomic-soliton setting.Comment: The final version, contains supplemental material, PRL (in press),
see
https://journals.aps.org/prl/accepted/71072YefTec1c16a44807625d0168f716b918fab
Two simple systems with cold atoms: quantum chaos tests and nonequilibrium dynamics
This article is an attempt to provide a link between the quantum
nonequilibrium dynamics of cold gases and fifty years of progress in the
lowdimensional quantum chaos. We identify two atomic systems lying on the
interface: two interacting atoms in a harmonic multimode waveguide and an
interacting two-component Bose-Bose mixture in a double-well potential. In
particular, we study the level spacing distribution, the wavefunction
statistics, the eigenstate thermalization, and the ability to thermalize in a
relaxation process as such.Comment: 18 pages, 9 figure
Multi-Channel Atomic Scattering and Confinement-Induced Resonances in Waveguides
We develop a grid method for multi-channel scattering of atoms in a waveguide
with harmonic confinement. This approach is employed to extensively analyze the
transverse excitations and deexcitations as well as resonant scattering
processes. Collisions of identical bosonic and fermionic as well as
distinguishable atoms in harmonic traps with a single frequency
permitting the center-of-mass (c.m.) separation are explored in depth. In the
zero-energy limit and single mode regime we reproduce the well-known
confinement-induced resonances (CIRs) for bosonic, fermionic and heteronuclear
collisions. In case of the multi-mode regime up to four open transverse
channels are considered. Previously obtained analytical results are extended
significantly here. Series of Feshbach resonances in the transmission behaviour
are identified and analyzed. The behaviour of the transmission with varying
energy and scattering lengths is discussed in detail. The dual CIR leading to a
complete quantum suppression of atomic scattering is revealed in multi-channel
scattering processes. Possible applications include, e.g., cold and ultracold
atom-atom collisions in atomic waveguides and electron-impurity scattering in
quantum wires.Comment: 35 pages, 18 figure