133 research outputs found
Finite temperature hydrodynamic modes of trapped quantum gases
The hydrodynamic equations of an ideal fluid formed by a dilute quantum gas
in a parabolic trapping potential are studied analytically and numerically. Due
to the appearance of internal modes in the fluid stratified by the trapping
potential, the spectrum of low-lying modes is found to be dense in the
high-temperature limit, with an infinitely degenerate set of zero-frequency
modes. The spectrum for Bose-fluids and Fermi-fluids is obtained and discussed.Comment: 26 pages, Late
Collective excitations of degenerate Fermi gases in anisotropic parabolic traps
The hydrodynamic low-frequency oscillations of highly degenerate Fermi gases
trapped in anisotropic harmonic potentials are investigated. Despite the lack
of an obvious spatial symmetry the wave-equation turns out to be separable in
elliptical coordinates, similar to a corresponding result established earlier
for Bose-condensates. This result is used to give the analytical solution of
the anisotropic wave equation for the hydrodynamic modes.Comment: 11 pages, Revte
Quantum states on supersymmetric minisuperspace with a cosmological constant
Spatially homogeneous models in quantum supergravity with a nonvanishing
cosmological constant are studied. A class of exact nontrivial solutions of the
supersymmetry and Lorentz constraints is obtained in terms of the Chern-Simons
action on the spatially homogeneous 3-manifold, both in Ashketar variables
where the solution is explicit up to reality conditions, and, more concretely,
in the tetrad-representation, where the solutions are given as integral
representations differing only by the contours of integration. In the limit of
a vanishing cosmological constant earlier exact solutions for Bianchi type IX
models in the tetrad-representation are recovered and additional asymmetric
solutions are found.Comment: 14 pages, late
Diffusion in normal and critical transient chaos
In this paper we investigate deterministic diffusion in systems which are
spatially extended in certain directions but are restricted in size and open in
other directions, consequently particles can escape. We introduce besides the
diffusion coefficient D on the chaotic repeller a coefficient which
measures the broadening of the distribution of trajectories during the
transient chaotic motion. Both coefficients are explicitly computed for
one-dimensional models, and they are found to be different in most cases. We
show furthermore that a jump develops in both of the coefficients for most of
the initial distributions when we approach the critical borderline where the
escape rate equals the Liapunov exponent of a periodic orbit.Comment: 4 pages Revtex file in twocolumn format with 2 included postscript
figure
Bose-Einstein condensation in shallow traps
In this paper we study the properties of Bose-Einstein condensates in shallow
traps. We discuss the case of a Gaussian potential, but many of our results
apply also to the traps having a small quadratic anharmonicity. We show the
errors introduced when a Gaussian potential is approximated with a parabolic
potential, these errors can be quite large for realistic optical trap parameter
values. We study the behavior of the condensate fraction as a function of trap
depth and temperature and calculate the chemical potential of the condensate in
a Gaussian trap. Finally we calculate the frequencies of the collective
excitations in shallow spherically symmetric and 1D traps.Comment: 6 pages, 4 figure
A New Method for Computing Topological Pressure
The topological pressure introduced by Ruelle and similar quantities describe
dynamical multifractal properties of dynamical systems. These are important
characteristics of mesoscopic systems in the classical regime. Original
definition of these quantities are based on the symbolic description of the
dynamics. It is hard or impossible to find symbolic description and generating
partition to a general dynamical system, therefore these quantities are often
not accessible for further studies. Here we present a new method by which the
symbolic description can be omitted. We apply the method for a mixing and an
intermittent system.Comment: 8 pages LaTeX with revtex.sty, the 4 postscript figures are included
using psfig.tex to appear in PR
Nonconcave entropies in multifractals and the thermodynamic formalism
We discuss a subtlety involved in the calculation of multifractal spectra
when these are expressed as Legendre-Fenchel transforms of functions analogous
to free energy functions. We show that the Legendre-Fenchel transform of a free
energy function yields the correct multifractal spectrum only when the latter
is wholly concave. If the spectrum has no definite concavity, then the
transform yields the concave envelope of the spectrum rather than the spectrum
itself. Some mathematical and physical examples are given to illustrate this
result, which lies at the root of the nonequivalence of the microcanonical and
canonical ensembles. On a more positive note, we also show that the
impossibility of expressing nonconcave multifractal spectra through
Legendre-Fenchel transforms of free energies can be circumvented with the help
of a generalized free energy function, which relates to a recently introduced
generalized canonical ensemble. Analogies with the calculation of rate
functions in large deviation theory are finally discussed.Comment: 9 pages, revtex4, 3 figures. Changes in v2: sections added on
applications plus many new references; contains an addendum not contained in
published versio
Bogoliubov theory of the Hawking effect in Bose-Einstein condensates
Artificial black holes may demonstrate some of the elusive quantum properties
of the event horizon, in particular Hawking radiation. One promising candidate
is a sonic hole in a Bose-Einstein condensate. We clarify why Hawking radiation
emerges from the condensate and how this condensed-matter analog reflects some
of the intriguing aspects of quantum black holes
Laser probing of Cooper-paired trapped atoms
We consider a gas of trapped Cooper-paired fermionic atoms which are
manipulated by laser light. The laser induces a transition from an internal
state with large negative scattering length (superfluid) to one with weaker
interactions (normal gas). We show that the process can be used to detect the
presence of the superconducting order parameter. Also, we propose a direct way
of measuring the size of the gap in the trap. The efficiency and feasibility of
this probing method is investigated in detail in different physical situations.Comment: 9 pages, 8 figure
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