897 research outputs found
Self-Trapping, Quantum Tunneling and Decay Rates for a Bose Gas with Attractive Nonlocal Interaction
We study the Bose-Einstein condensation for a cloud of Li atoms with
attractive nonlocal (finite-range) interaction in a harmonic trap. In addition
to the low-density metastable branch, that is present also in the case of local
interaction, a new stable branch appears at higher densities. For a large
number of atoms, the size of the cloud in the stable high-density branch is
independent of the trap size and the atoms are in a macroscopic quantum
self-trapped configuration. We analyze the macroscopic quantum tunneling
between the low-density metastable branch and the high-density one by using the
istanton technique. Moreover we consider the decay rate of the Bose condensate
due to inelastic two- and three-body collisions.Comment: 5 pages, 4 figures, submitted to Phys. Rev.
Instantons and radial excitations in attractive Bose-Einstein condensates
Imaginary- and real-time versions of an equation for the condensate density
are presented which describe dynamics and decay of any spherical Bose-Einstein
condensate (BEC) within the mean field appraoch. We obtain quantized energies
of collective finite amplitude radial oscillations and exact numerical
instanton solutions which describe quantum tunneling from both the metastable
and radially excited states of the BEC of 7Li atoms. The mass parameter for the
radial motion is found different from the gaussian value assumed hitherto, but
the effect of this difference on decay exponents is small. The collective
breathing states form slightly compressed harmonic spectrum, n=4 state lying
lower than the second Bogolyubov (small amplitude) mode. The decay of these
states, if excited, may simulate a shorter than true lifetime of the metastable
state. By scaling arguments, results extend to other attractive BEC-s.Comment: 6 pages, 3 figure
Anomalies in orbifold field theories
We study the constraints on models with extra dimensions arising from local
anomaly cancellation. We consider a five-dimensional field theory with a U(1)
gauge field and a charged fermion, compactified on the orbifold S^1/(Z_2 x
Z_2'). We show that, even if the orbifold projections remove both fermionic
zero modes, there are gauge anomalies localized at the fixed points. Anomalies
naively cancel after integration over the fifth dimension, but gauge invariance
is broken, spoiling the consistency of the theory. We discuss the implications
for realistic supersymmetric models with a single Higgs hypermultiplet in the
bulk, and possible cancellation mechanisms in non-minimal models.Comment: 10 pages, 2 figures, LaTex; v2: final version to be published in
Phys. Lett.
Fredholm Determinants, Differential Equations and Matrix Models
Orthogonal polynomial random matrix models of NxN hermitian matrices lead to
Fredholm determinants of integral operators with kernel of the form (phi(x)
psi(y) - psi(x) phi(y))/x-y. This paper is concerned with the Fredholm
determinants of integral operators having kernel of this form and where the
underlying set is a union of open intervals. The emphasis is on the
determinants thought of as functions of the end-points of these intervals. We
show that these Fredholm determinants with kernels of the general form
described above are expressible in terms of solutions of systems of PDE's as
long as phi and psi satisfy a certain type of differentiation formula. There is
also an exponential variant of this analysis which includes the circular
ensembles of NxN unitary matrices.Comment: 34 pages, LaTeX using RevTeX 3.0 macros; last version changes only
the abstract and decreases length of typeset versio
On Charge Quantization and Abelian Gauge Horizontal Symmetries
Under the assumption that there exists a local gauge horizontal symmetry
wich allows only for a top quark mass at tree level, we look for the
constraints that charge quatization and the family structure of the standard
model imposes on that symmetry.Comment: 13 pages, LaTeX, Acepted in Physics Letters
Mean-field analysis of collapsing and exploding Bose-Einstein condensates
The dynamics of collapsing and exploding trapped Bose-Einstein condensat es
caused by a sudden switch of interactions from repulsive to attractive a re
studied by numerically integrating the Gross-Pitaevskii equation with atomic
loss for an axially symmetric trap. We investigate the decay rate of
condensates and the phenomena of bursts and jets of atoms, and compare our
results with those of the experiments performed by E. A. Donley {\it et al.}
[Nature {\bf 412}, 295 (2001)]. Our study suggests that the condensate decay
and the burst production is due to local intermittent implosions in the
condensate, and that atomic clouds of bursts and jets are coherent. We also
predict nonlinear pattern formation caused by the density instability of
attractive condensates.Comment: 7 pages, 8 figures, axi-symmetric results are adde
Superconducting fluctuations in the Luther-Emery liquid
The single-particle superconducting Green's functions of a Luther-Emery
liquid is computed by bosonization techniques. Using a formulation introduced
by Poilblanc and Scalapino [Phys. Rev. B v. 66, art. 052513 (2002)], an
asymptotic expression of the superconducting gap is deduced in the long
wavelength and small frequency limit. Due to superconducting phase
fluctuations, the gap exhibits as a function of size L a (1/L)^{1/2K_\rho}
power-law decay as well as an interesting singularity at the spectral gap
energy. Similarities and differences with the 2-leg t-J ladder are outlined.Comment: RevTeX 4, 3 pages, 2 EPS figure
Relativistic effects and quasipotential equations
We compare the scattering amplitude resulting from the several quasipotential
equations for scalar particles. We consider the Blankenbecler-Sugar, Spectator,
Thompson, Erkelenz-Holinde and Equal-Time equations, which were solved
numerically without decomposition into partial waves. We analyze both
negative-energy state components of the propagators and retardation effects. We
found that the scattering solutions of the Spectator and the Equal-Time
equations are very close to the nonrelativistic solution even at high energies.
The overall relativistic effect increases with the energy. The width of the
band for the relative uncertainty in the real part of the scattering
matrix, due to different dynamical equations, is largest for
backward-scattering angles where it can be as large as 40%.Comment: Accepted for publication in Phys. Rev.
Travelling waves for the Gross-Pitaevskii equation II
The purpose of this paper is to provide a rigorous mathematical proof of the
existence of travelling wave solutions to the Gross-Pitaevskii equation in
dimensions two and three. Our arguments, based on minimization under
constraints, yield a full branch of solutions, and extend earlier results,
where only a part of the branch was built. In dimension three, we also show
that there are no travelling wave solutions of small energy.Comment: Final version accepted for publication in Communications in
Mathematical Physics with a few minor corrections and added remark
Measurement of the space-time interval between two events using the retarded and advanced times of each event with respect to a time-like world-line
Several recent studies have been devoted to investigating the limitations
that ordinary quantum mechanics and/or quantum gravity might impose on the
measurability of space-time observables. These analyses are often confined to
the simplified context of two-dimensional flat space-time and rely on a simple
procedure for the measurement of space-like distances based on the exchange of
light signals. We present a generalization of this measurement procedure
applicable to all three types of space-time intervals between two events in
space-times of any number of dimensions. We also present some preliminary
observations on an alternative measurement procedure that can be applied taking
into account the gravitational field of the measuring apparatus, and briefly
discuss quantum limitations of measurability in this context.Comment: 17 page
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