15 research outputs found
Excitation spectrum of a 2D long-range Bose-liquid with a supersymmetry
We have studied excitation spectrum of the specfic 2D model of strongly
interacting Bose particles via mapping of the many-body Schrodinger equation in
imaginary time to the classical stochastic dynamics. In a broad range of
coupling strength a roton-like spectrum is found, with the roton gap
being extremely small in natural units. A single quantum phase transition
between strongly correlated supefluid and quantum Berezinsky crystal is found.Comment: 6 pages, 6 figure
Wave turbulence in Bose-Einstein condensates
The kinetics of nonequilibrium Bose-Einstein condensates are considered
within the framework of the Gross-Pitaevskii equation. A systematic derivation
is given for weak small-scale perturbations of a steady confined condensate
state. This approach combines a wavepacket WKB description with the weak
turbulence theory. The WKB theory derived in this paper describes the effect of
the condensate on the short-wave excitations which appears to be different from
a simple renormalization of the confining potential suggested in previous
literature.Comment: 33 pages 2 figure
Atom loss and the formation of a molecular Bose-Einstein condensate by Feshbach resonance
In experiments conducted recently at MIT on Na Bose-Einstein condensates [S.
Inouye et al, Nature 392, 151 (1998); J. Stenger et al, Phys. Rev. Lett. 82,
2422 (1999)], large loss rates were observed when a time-varying magnetic field
was used to tune a molecular Feshbach resonance state near the state of a pair
of atoms in the condensate. A collisional deactivation mechanism affecting a
temporarily formed molecular condensate [see V. A. Yurovsky, A. Ben-Reuven, P.
S. Julienne and C. J. Williams, Phys. Rev. A 60, R765 (1999)], studied here in
more detail, accounts for the results of the slow-sweep experiments. A best fit
to the MIT data yields a rate coefficient for deactivating atom-molecule
collisions of 1.6e-10 cm**3/s. In the case of the fast sweep experiment, a
study is carried out of the combined effect of two competing mechanisms, the
three-atom (atom-molecule) or four-atom (molecule-molecule) collisional
deactivation vs. a process of two-atom trap-state excitation by curve crossing
[F. H. Mies, P. S. Julienne, and E. Tiesinga, Phys. Rev. A 61, 022721 (2000)].
It is shown that both mechanisms contribute to the loss comparably and
nonadditively.Comment: LaTeX, 14 pages, 12 PostScript figures, uses REVTeX and psfig,
submitted to Physical Review
The Response to a Perturbation in the Reflection Amplitude
We apply inverse scattering theory to calculate the functional derivative of
the potential and wave function of a one-dimensional
Schr\"odinger operator with respect to the reflection amplitude .Comment: 16 pages, no figure
Stability and collapse of localized solutions of the controlled three-dimensional Gross-Pitaevskii equation
On the basis of recent investigations, a newly developed analytical procedure
is used for constructing a wide class of localized solutions of the controlled
three-dimensional (3D) Gross-Pitaevskii equation (GPE) that governs the
dynamics of Bose-Einstein condensates (BECs). The controlled 3D GPE is
decomposed into a two-dimensional (2D) linear Schr\"{o}dinger equation and a
one-dimensional (1D) nonlinear Schr\"{o}dinger equation, constrained by a
variational condition for the controlling potential. Then, the above class of
localized solutions are constructed as the product of the solutions of the
transverse and longitudinal equations. On the basis of these exact 3D
analytical solutions, a stability analysis is carried out, focusing our
attention on the physical conditions for having collapsing or non-collapsing
solutions.Comment: 21 pages, 14 figure
Freely decaying turbulence and Bose-Einstein condensation in Gross-Pitaevski model
We study turbulence and Bose-Einstein condensation (BEC) within the two-dimensional Gross-Pitaevski (GP) model. In the present work, we compute decaying GP turbulence in order to establish whether BEC can occur without forcing and if there is an intensity threshold for this process. We use the wavenumber-frequency plots which allow us to clearly separate the condensate and the wave components and, therefore, to conclude if BEC is present. We observe that BEC in such a system happens even for very weakly nonlinear initial conditions without any visible threshold. BEC arises via a growing phase coherence due to anihilation of phase defects/vortices. We study this process by tracking of propagating vortex pairs. The pairs loose momentum by scattering the background sound, which results in gradual decrease of the distance between the vortices. Occasionally, vortex pairs collide with a third vortex thereby emitting sound, which can lead to more sudden shrinking of the pairs. After the vortex anihilation the pulse propagates further as a dark soliton, and it eventually bursts creating a shock