27 research outputs found
Ideal quantum gases in two dimensions
Thermodynamic properties of non-relativistic bosons and fermions in two
spatial dimensions and without interactions are derived. All the virial
coefficients are the same except for the second, for which the signs are
opposite. This results in the same specific heat for the two gases. Existing
equations of state for the free anyon gas are also discussed and shown to break
down at low temperatures or high densities.Comment: 17 page
Thermodynamics of a weakly interacting Bose-Einstein gas
The one-loop effective potential for non-relativistic bosons with a delta
function repulsive potential is calculated for a given chemical potential using
functional methods. After renormalization and at zero temperature it reproduces
the standard ground state energy and pressureas function of the particle
density. At finite temperatures it is found necessary to include ring
corrections to the one-loop result in order to satisfy the Goldstone theorem.
It is natural to introduce an effective chemical potential directly related to
the order parameter and which uniformly decreases with increasing temperatures.
This is in contrast to the the ordinary chemical potential which peaks at the
critical temperature. The resulting thermodynamics in the condensed phase at
very low temperatures is found to be the same as in the Bogoliubov
approximation where the degrees of freedom are given by the Goldstone bosons.
At higher temperatures the ring corrections dominate and result in a critical
temperature unaffected by the interaction.Comment: 39 pages, 9 figures, picTex, submitted to Annals of Physics.
Discussions on renormalization and off-diagonal self energies are made
clearer in this version. A short derivation of the non-relativistic limit is
adde
Localizing fields on brane in magnetized backgound
To localize the scalar, fermion, and abelian gauge fields on our 3-brane, a
simple mechanism with a hypothetical "magnetic field" in the bulk is proposed.
This mechanism is to treat all fields in the equal footing without ad hoc
consideration. In addition, the machanism can be easily realized in a flat
dimension six Minkowski space and it works even in the weak coupling limit
Nonergodic Behavior of Interacting Bosons in Harmonic Traps
We study the time evolution of a system of interacting bosons in a harmonic
trap. In the low-energy regime, the quantum system is not ergodic and displays
rather large fluctuations of the ground state occupation number. In the high
energy regime of classical physics we find nonergodic behavior for modest
numbers of trapped particles. We give two conditions that assure the ergodic
behavior of the quantum system even below the condensation temperature.Comment: 11 pages, 3 PS-figures, uses psfig.st
Semiclassical Corrections to a Static Bose-Einstein Condensate at Zero Temperature
In the mean-field approximation, a trapped Bose-Einstein condensate at zero
temperature is described by the Gross-Pitaevskii equation for the condensate,
or equivalently, by the hydrodynamic equations for the number density and the
current density. These equations receive corrections from quantum field
fluctuations around the mean field. We calculate the semiclassical corrections
to these equations for a general time-independent state of the condensate,
extending previous work to include vortex states as well as the ground state.
In the Thomas-Fermi limit, the semiclassical corrections can be taken into
account by adding a local correction term to the Gross-Pitaevskii equation. At
second order in the Thomas-Fermi expansion, the semiclassical corrections can
be taken into account by adding local correction terms to the hydrodynamic
equations
Exclusion Statistics in a trapped two-dimensional Bose gas
We study the statistical mechanics of a two-dimensional gas with a repulsive
delta function interaction, using a mean field approximation. By a direct
counting of states we establish that this model obeys exclusion statistics and
is equivalent to an ideal exclusion statistics gas.Comment: 3 pages; minor changes in notation; typos correcte
Stability of the homogeneous Bose-Einstein condensate at large gas parameter
The properties of the uniform Bose gas is studied within the optimized
variational perturbation theory (Gaussian approximation) in a self-consistent
way. It is shown that the atomic BEC with a repulsive interaction becomes
unstable when the gas parameter gamma=rho a^3 exceeds a critical value
gamma_{crit} ~ 0.01. The quantum corrections beyond the Bogoliubov-Popov
approximation to the energy density, chemical potential and pressure in powers
of gamma expansions are presented.Comment: 9 pages, 3 figures, Revte
Bose-Einstein condensation in a one-dimensional interacting system due to power-law trapping potentials
We examine the possibility of Bose-Einstein condensation in one-dimensional
interacting Bose gas subjected to confining potentials of the form , in which , by solving the
Gross-Pitaevskii equation within the semi-classical two-fluid model. The
condensate fraction, chemical potential, ground state energy, and specific heat
of the system are calculated for various values of interaction strengths. Our
results show that a significant fraction of the particles is in the lowest
energy state for finite number of particles at low temperature indicating a
phase transition for weakly interacting systems.Comment: LaTeX, 6 pages, 8 figures, uses grafik.sty (included), to be
published in Phys. Rev.
Bose-Einstein condensation in arbitrarily shaped cavities
We discuss the phenomenon of Bose-Einstein condensation of an ideal
non-relativistic Bose gas in an arbitrarily shaped cavity. The influence of the
finite extension of the cavity on all thermodynamical quantities, especially on
the critical temperature of the system, is considered. We use two main methods
which are shown to be equivalent. The first deals with the partition function
as a sum over energy levels and uses a Mellin-Barnes integral representation to
extract an asymptotic formula. The second method converts the sum over the
energy levels to an integral with a suitable density of states factor obtained
from spectral analysis. The application to some simple cavities is discussed.Comment: 10 pages, LaTeX, to appear in Physical Review