116 research outputs found
Quantum Kinetic Theory V: Quantum kinetic master equation for mutual interaction of condensate and noncondensate
A detailed quantum kinetic master equation is developed which couples the
kinetics of a trapped condensate to the vapor of non-condensed particles. This
generalizes previous work which treated the vapor as being undepleted.Comment: RevTeX, 26 pages and 5 eps figure
A particle-number-conserving Bogoliubov method which demonstrates the validity of the time-dependent Gross-Pitaevskii equation for a highly condensed Bose gas
The Bogoliubov method for the excitation spectrum of a Bose-condensed gas is
generalized to apply to a gas with an exact large number of particles.
This generalization yields a description of the Schr\"odinger picture field
operators as the product of an annihilation operator for the total number
of particles and the sum of a ``condensate wavefunction'' and a phonon
field operator in the form when the field operator acts on the N particle subspace. It
is then possible to expand the Hamiltonian in decreasing powers of ,
an thus obtain solutions for eigenvalues and eigenstates as an asymptotic
expansion of the same kind. It is also possible to compute all matrix elements
of field operators between states of different N.Comment: RevTeX, 11 page
Ideal Stars and General Relativity
We study a system of differential equations that governs the distribution of
matter in the theory of General Relativity. The new element in this paper is
the use of a dynamical action principle that includes all the degrees of
freedom, matter as well as metric. The matter lagrangian defines a relativistic
version of non-viscous, isentropic hydrodynamics. The matter fields are a
scalar density and a velocity potential; the conventional, four-vector velocity
field is replaced by the gradient of the potential and its scale is fixed by
one of the eulerian equations of motion, an innovation that significantly
affects the imposition of boundary conditions. If the density is integrable at
infinity, then the metric approaches the Schwarzschild metric at large
distances. There are stars without boundary and with finite total mass; the
metric shows rapid variation in the neighbourhood of the Schwarzschild radius
and there is a very small core where a singularity indicates that the gas laws
break down. For stars with boundary there emerges a new, critical relation
between the radius and the gravitational mass, a consequence of the stronger
boundary conditions. Tentative applications are suggested, to certain Red
Giants, and to neutron stars, but the investigation reported here was limited
to polytropic equations of state. Comparison with the results of Oppenheimer
and Volkoff on neutron cores shows a close agreement of numerical results.
However, in the model the boundary of the star is fixed uniquely by the
required matching of the interior metric to the external Schwarzschild metric,
which is not the case in the traditional approach.Comment: 26 pages, 7 figure
Quantum Kinetic Theory III: Quantum kinetic master equation for strongly condensed trapped systems
We extend quantum kinetic theory to deal with a strongly Bose-condensed
atomic vapor in a trap. The method assumes that the majority of the vapor is
not condensed, and acts as a bath of heat and atoms for the condensate. The
condensate is described by the particle number conserving Bogoliubov method
developed by one of the authors. We derive equations which describe the
fluctuations of particle number and phase, and the growth of the Bose-Einstein
condensate. The equilibrium state of the condensate is a mixture of states with
different numbers of particles and quasiparticles. It is not a quantum
superposition of states with different numbers of particles---nevertheless, the
stationary state exhibits the property of off-diagonal long range order, to the
extent that this concept makes sense in a tightly trapped condensate.Comment: 3 figures submitted to Physical Review
Damped Bogoliubov excitations of a condensate interacting with a static thermal cloud
We calculate the damping of condensate collective excitations at finite
temperatures arising from the lack of equilibrium between the condensate and
thermal atoms. We neglect the non-condensate dynamics by fixing the thermal
cloud in static equilibrium. We derive a set of generalized Bogoliubov
equations for finite temperatures that contain an explicit damping term due to
collisional exchange of atoms between the two components. We have numerically
solved these Bogoliubov equations to obtain the temperature dependence of the
damping of the condensate modes in a harmonic trap. We compare these results
with our recent work based on the Thomas-Fermi approximation.Comment: 9 pages, 3 figures included. Submitted to PR
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
The Bogoliubov Theory of a BEC in Particle Representation
In the number-conserving Bogoliubov theory of BEC the Bogoliubov
transformation between quasiparticles and particles is nonlinear. We invert
this nonlinear transformation and give general expression for eigenstates of
the Bogoliubov Hamiltonian in particle representation. The particle
representation unveils structure of a condensate multiparticle wavefunction. We
give several examples to illustrate the general formalism.Comment: 10 pages, 9 figures, version accepted for publication in Phys. Rev.
Approach to the semiconductor cavity QED in high-Q regimes with q-deformed boson
The high density Frenkel exciton which interacts with a single mode
microcavity field is dealed with in the framework of the q-deformed boson. It
is shown that the q-defomation of bosonic commutation relations is satisfied
naturally by the exciton operators when the low density limit is deviated. An
analytical expression of the physical spectrum for the exciton is given by
using of the dressed states of the cavity field and the exciton. We also give
the numerical study and compare the theoretical results with the experimental
resultsComment: 6 pages, 2 figure
Sterile neutrino production via active-sterile oscillations: the quantum Zeno effect
We study several aspects of the kinetic approach to sterile neutrino
production via active-sterile mixing. We obtain the neutrino propagator in the
medium including self-energy corrections up to , from which
we extract the dispersion relations and damping rates of the propagating modes.
The dispersion relations are the usual ones in terms of the index of refraction
in the medium, and the damping rates are where
is the active neutrino scattering rate and
is the mixing angle in the medium. We provide a generalization of
the transition probability in the \emph{medium from expectation values in the
density matrix}: and
study the conditions for its quantum Zeno suppression directly in real time. We
find the general conditions for quantum Zeno suppression, which for sterile neutrinos with \emph{may
only be} fulfilled near an MSW resonance. We discuss the implications for
sterile neutrino production and argue that in the early Universe the wide
separation of relaxation scales far away from MSW resonances suggests the
breakdown of the current kinetic approach.Comment: version to appear in JHE
Condensate fluctuations in finite Bose-Einstein condensates at finite temperature
A Langevin equation for the complex amplitude of a single-mode Bose-Einstein
condensate is derived. The equation is first formulated phenomenologically,
defining three transport parameters. It is then also derived microscopically.
Expressions for the transport parameters in the form of Green-Kubo formulas are
thereby derived and evaluated for simple trap geometries, a cubic box with
cyclic boundary conditions and an isotropic parabolic trap. The number
fluctuations in the condensate, their correlation time, and the
temperature-dependent collapse-time of the order parameter as well as its
phase-diffusion coefficient are calculated.Comment: 29 pages, Revtex, to appear in Phys.Rev.
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