540 research outputs found
Representative Ensembles in Statistical Mechanics
The notion of representative statistical ensembles, correctly representing
statistical systems, is strictly formulated. This notion allows for a proper
description of statistical systems, avoiding inconsistencies in theory. As an
illustration, a Bose-condensed system is considered. It is shown that a
self-consistent treatment of the latter, using a representative ensemble,
always yields a conserving and gapless theory.Comment: Latex file, 18 page
Bose-Einstein-condensed gases in arbitrarily strong random potentials
Bose-Einstein-condensed gases in external spatially random potentials are
considered in the frame of a stochastic self-consistent mean-field approach.
This method permits the treatment of the system properties for the whole range
of the interaction strength, from zero to infinity, as well as for arbitrarily
strong disorder. Besides a condensate and superfluid density, a glassy number
density due to a spatially inhomogeneous component of the condensate occurs.
For very weak interactions and sufficiently strong disorder, the superfluid
fraction can become smaller than the condensate fraction, while at relatively
strong interactions, the superfluid fraction is larger than the condensate
fraction for any strength of disorder. The condensate and superfluid fractions,
and the glassy fraction always coexist, being together either nonzero or zero.
In the presence of disorder, the condensate fraction becomes a nonmonotonic
function of the interaction strength, displaying an antidepletion effect caused
by the competition between the stabilizing role of the atomic interaction and
the destabilizing role of the disorder. With increasing disorder, the
condensate and superfluid fractions jump to zero at a critical value of the
disorder parameter by a first-order phase transition
Polaron Energy Spectrum in Quantum Dots
Energy spectrum of a weak coupling polaron is considered in a cylindrical
quantum dot. An analytical expression for the polaron energy shift is obtained
using a modified pertubation theory.Comment: 7 pages, IOP style LaTeX fil
Condensate and superfluid fractions for varying interactions and temperature
A system with Bose-Einstein condensate is considered in the frame of the
self-consistent mean-field approximation, which is conserving, gapless, and
applicable for arbitrary interaction strengths and temperatures. The main
attention is paid to the thorough analysis of the condensate and superfluid
fractions in a wide region of interaction strengths and for all temperatures
between zero and the critical point T_c. The normal and anomalous averages are
shown to be of the same order for almost all interactions and temperatures,
except the close vicinity of T_c. But even in the vicinity of the critical
temperature, the anomalous average cannot be neglected, since only in the
presence of the latter the phase transition at T_c becomes of second order, as
it should be. Increasing temperature influences the condensate and superfluid
fractions in a similar way, by diminishing them. But their behavior with
respect to the interaction strength is very different. For all temperatures,
the superfluid fraction is larger than the condensate fraction. These coincide
only at T_c or under zero interactions. For asymptotically strong interactions,
the condensate is almost completely depleted, even at low temperatures, while
the superfluid fraction can be close to one.Comment: Latex file, 22 pages, 5 figure
Gravitational oscillations in multidimensional anisotropic model with cosmological constant and their contributions into the energy of vacuum
Were studied classical oscillations of background metric in the
multidimensional anisotropic model of Kazner in the de-Sitter stage. Obtained
dependence of fluctuations on dimension of space-time with infinite expansion.
Stability of the model could be achieved when number of space-like dimensions
equals or more then four. Were calculated contributions to the density of
"vacuum energy", that are providing by proper oscillations of background metric
and compared with contribution of cosmological arising of particles due to
expansion. As it turned out, contribution of gravitational oscillation of
metric into density of "vacuum energy" should play significant role in the
de-Sitter stage
Relativistic Einstein-Podolsky-Rosen correlations for vector and tensor states
We calculate and investigate the relativistic correlation function for
bipartite systems of spin-1/2 in vector and spin-1 particles in tensor states.
We show that the relativistic correlation function, which depends on particles
momenta, may have local extrema. What is more, the momentum dependance of the
correlation functions for two choices of relativistic spin operator may be
significantly different.Comment: 7 pages, 7 figure
Optimal trap shape for a Bose gas with attractive interactions
Dilute Bose gas with attractive interactions is considered at zero
temperature, when practically all atoms are in Bose-Einstein condensate. The
problem is addressed aiming at answering the question: What is the optimal trap
shape allowing for the condensation of the maximal number of atoms with
negative scattering lengths? Simple and accurate analytical formulas are
derived allowing for an easy analysis of the optimal trap shapes. These
analytical formulas are the main result of the paper.Comment: Latex file, 21 page
Transformation laws of the components of classical and quantum fields and Heisenberg relations
The paper recalls and point to the origin of the transformation laws of the
components of classical and quantum fields. They are considered from the
"standard" and fibre bundle point of view. The results are applied to the
derivation of the Heisenberg relations in quite general setting, in particular,
in the fibre bundle approach. All conclusions are illustrated in a case of
transformations induced by the Poincar\'e group.Comment: 22 LaTeX pages. The packages AMS-LaTeX and amsfonts are required. For
other papers on the same topic, view http://theo.inrne.bas.bg/~bozho/ . arXiv
admin note: significant text overlap with arXiv:0809.017
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