652 research outputs found
Beyond mean-field dynamics of small Bose-Hubbard systems based on the number-conserving phase space approach
The number-conserving quantum phase space description of the Bose-Hubbard
model is discussed for the illustrative case of two and three modes, as well as
the generalization of the two-mode case to an open quantum system. The
phase-space description based on generalized SU(M) coherent states yields a
Liouvillian flow in the macroscopic limit, which can be efficiently simulated
using Monte Carlo methods even for large systems. We show that this description
clearly goes beyond the common mean-field limit. In particular it resolves
well-known problems where the common mean-field approach fails, like the
description of dynamical instabilities and chaotic dynamics. Moreover, it
provides a valuable tool for a semi-classical approximation of many interesting
quantities, which depend on higher moments of the quantum state and are
therefore not accessible within the common approach. As a prominent example, we
analyse the depletion and heating of the condensate. A comparison to methods
ignoring the fixed particle number shows that in this case artificial number
fluctuations lead to ambiguities and large deviations even for quite simple
examples.Comment: Significantly enhanced and revised version (20 pages, 20 figures
Chaotic Quantum Decay in Driven Biased Optical Lattices
Quantum decay in an ac driven biased periodic potential modeling cold atoms
in optical lattices is studied for a symmetry broken driving. For the case of
fully chaotic classical dynamics the classical exponential decay is quantum
mechanically suppressed for a driving frequency \omega in resonance with the
Bloch frequency \omega_B, q\omega=r\omega_B with integers q and r.
Asymptotically an algebraic decay ~t^{-\gamma} is observed. For r=1 the
exponent \gamma agrees with as predicted by non-Hermitian random matrix
theory for q decay channels. The time dependence of the survival probability
can be well described by random matrix theory. The frequency dependence of the
survival probability shows pronounced resonance peaks with sub-Fourier
character.Comment: 7 pages, 5 figure
Resonance solutions of the nonlinear Schr\"odinger equation in an open double-well potential
The resonance states and the decay dynamics of the nonlinear Schr\"odinger
(or Gross-Pitaevskii) equation are studied for a simple, however flexible model
system, the double delta-shell potential. This model allows analytical
solutions and provides insight into the influence of the nonlinearity on the
decay dynamics. The bifurcation scenario of the resonance states is discussed,
as well as their dynamical stability properties. A discrete approximation using
a biorthogonal basis is suggested which allows an accurate description even for
only two basis states in terms of a nonlinear, nonhermitian matrix problem.Comment: 21 pages, 14 figure
Kicked Bose-Hubbard systems and kicked tops -- destruction and stimulation of tunneling
In a two-mode approximation, Bose-Einstein condensates (BEC) in a double-well
potential can be described by a many particle Hamiltonian of Bose-Hubbard type.
We focus on such a BEC whose interatomic interaction strength is modulated
periodically by -kicks which represents a realization of a kicked top.
In the (classical) mean-field approximation it provides a rich mixed phase
space dynamics with regular and chaotic regions. By increasing the
kick-strength a bifurcation leads to the appearance of self-trapping states
localized on regular islands. This self-trapping is also found for the many
particle system, however in general suppressed by coherent many particle
tunneling oscillations. The tunneling time can be calculated from the
quasi-energy splitting of the corresponding Floquet states. By varying the
kick-strength these quasi-energy levels undergo both avoided and even actual
crossings. Therefore stimulation or complete destruction of tunneling can be
observed for this many particle system
Exact number conserving phase-space dynamics of the M-site Bose-Hubbard model
The dynamics of M-site, N-particle Bose-Hubbard systems is described in
quantum phase space constructed in terms of generalized SU(M) coherent states.
These states have a special significance for these systems as they describe
fully condensed states. Based on the differential algebra developed by Gilmore,
we derive an explicit evolution equation for the (generalized) Husimi-(Q)- and
Glauber-Sudarshan-(P)-distributions. Most remarkably, these evolution equations
turn out to be second order differential equations where the second order terms
scale as 1/N with the particle number. For large N the evolution reduces to a
(classical) Liouvillian dynamics. The phase space approach thus provides a
distinguished instrument to explore the mean-field many-particle crossover. In
addition, the thermodynamic Bloch equation is analyzed using similar
techniques.Comment: 11 pages, Revtex
Quantum dynamics of Bose-Einstein condensates in tilted and driven bichromatic optical lattices
We study the dynamics of Bose-Einstein condensates in tilted and driven
optical superlattices. For a bichromatic lattice, each Bloch band split up into
two minibands such that the dynamics is governed by the interplay of Bloch
oscillations and transitions between the bands. Thus, bichromatic potentials
provide an excellent model system for the study of nonlinear Landau-Zener
tunneling and allow for a variety of applications in matter wave interferometry
and quantum metrology. In the present paper we investigate the coherent
dynamics of an interacting Bose-Einstein condensate as well as its stability.
Different mechanisms of instability are discussed, which lead to a rapid
depletion of the condensate.Comment: 9 pages, 9 figures, to appear in Phys. Rev.
An analytical study of resonant transport of Bose-Einstein condensates
We study the stationary nonlinear Schr\"odinger equation, or Gross-Pitaevskii
equation, for a one--dimensional finite square well potential. By neglecting
the mean--field interaction outside the potential well it is possible to
discuss the transport properties of the system analytically in terms of ingoing
and outgoing waves. Resonances and bound states are obtained analytically. The
transmitted flux shows a bistable behaviour. Novel crossing scenarios of
eigenstates similar to beak--to--beak structures are observed for a repulsive
mean-field interaction. It is proven that resonances transform to bound states
due to an attractive nonlinearity and vice versa for a repulsive nonlinearity,
and the critical nonlinearity for the transformation is calculated
analytically. The bound state wavefunctions of the system satisfy an
oscillation theorem as in the case of linear quantum mechanics. Furthermore,
the implications of the eigenstates on the dymamics of the system are
discussed.Comment: RevTeX4, 16 pages, 19 figure
Sequence of Potentials Lying Between the U(5) and X(5) Symmetries
Starting from the original collective Hamiltonian of Bohr and separating the
beta and gamma variables as in the X(5) model of Iachello, an exactly soluble
model corresponding to a harmonic oscillator potential in the beta-variable (to
be called X(5)-) is constructed. Furthermore, it is proved that the
potentials of the form (with n being integer) provide a ``bridge''
between this new X(5)- model (occuring for n=1) and the X(5) model
(corresponding to an infinite well potential in the beta-variable, materialized
for n going to infinity. Parameter-free (up to overall scale factors)
predictions for spectra and B(E2) transition rates are given for the potentials
, , , , corresponding to E(4)/E(2) ratios
of 2.646, 2.769, 2.824, and 2.852 respectively, compared to the E(4)/E(2)
ratios of 2.000 for U(5) and 2.904 for X(5). Hints about nuclei showing this
behaviour, as well as about potentials ``bridging'' the X(5) symmetry with
SU(3) are briefly discussed.Comment: 18 pages, LaTeX, 5 postscript figure
Spiral ganglions and speech perception in the elderly. Which turn of the cochlea is the more relevant? a preliminary study on human temporal bones
OBJECTIVES: To identify the cochlear segment in which spiral ganglion neuron (SGN) loss may more severely impact discrimination thresholds. MATERIALS and METHODS: Thirteen temporal bones from 13 subjects between 55 and 77 years of age were analyzed. The organ of corti was analyzed to identify the loss of hair cells, and the number of SGNs in each cochlear segment were counted. The results of the speech perception test (SPT) and pure tone audiometry (PTA) tests were collected. PTA averages for low and high frequencies were calculated. One-way analysis of variance (ANOVA), Pearson, Spearman, and multilinear regression tests were performed. RESULTS: No statistically significant correlation was identified between the patient’s age and number of SGNs. Statistically significant differences were observed between the number of SGNs in the different cochlear segments (one-way ANOVA: p<0.0001) and between poor PTA average and SPT scores (negative correlation) (p=0.03). A statistically significant correlation was identified between the overall number of cochlear SGNs and SPT scores (p=0.02) and between the number of SGNs in cochlear segments I (p=0.04) and II and the SPT score (p=0.03). CONCLUSIONS: We identified that residual SGNs in the basal and middle turns of the cochlea might be determinants of speech perception
- …