418 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
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
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
Bose-Einstein-condensed systems in random potentials
The properties of systems with Bose-Einstein condensate in external
time-independent random potentials are investigated in the frame of a
self-consistent stochastic mean-field approximation. General considerations are
presented, which are valid for finite temperatures, arbitrary strengths of the
interaction potential, and for arbitrarily strong disorder potentials. The
special case of a spatially uncorrelated random field is then treated in more
detail. It is shown that the system consists of three components, condensed
particles, uncondensed particles and a glassy density fraction, but that the
pure Bose glass phase with only a glassy density does not appear. The theory
predicts a first-order phase transition for increasing disorder parameter,
where the condensate fraction and the superfluid fraction simultaneously jump
to zero. The influence of disorder on the ground-state energy, the stability
conditions, the compressibility, the structure factor, and the sound velocity
are analyzed. The uniform ideal condensed gas is shown to be always
stochastically unstable, in the sense that an infinitesimally weak disorder
destroys the Bose-Einstein condensate, returning the system to the normal
state. But the uniform Bose-condensed system with finite repulsive interactions
becomes stochastically stable and exists in a finite interval of the disorder
parameter.Comment: Latex file, final published varian
From Light Nuclei to Nuclear Matter. The Role of Relativity?
The success of non-relativistic quantum dynamics in accounting for the
binding energies and spectra of light nuclei with masses up to A=10 raises the
question whether the same dynamics applied to infinite nuclear matter agrees
with the empirical saturation properties of large nuclei.The simple unambiguous
relation between few-nucleon and many-nucleon Hamiltonians is directly related
to the Galilean covariance of nonrelativistic dynamics. Relations between the
irreducible unitary representations of the Galilei and Poincare groups indicate
thatthe ``nonrelativistic'' nuclear Hamiltonians may provide sufficiently
accurate approximations to Poincare invariant mass operators. In relativistic
nuclear dynamics based on suitable Lagrangeans the intrinsic nucleon parity is
an explicit, dynamically relevant, degree of freedom and the emphasis is on
properties of nuclear matter. The success of this approach suggests the
question how it might account for the spectral properties of light nuclei.Comment: conference proceedings "The 11th International Conference on Recent
Progress in Many-Body Theories" to be published by World Scientifi
Space Symmetries and Quantum Behavior of Finite Energy Configurations in SU(2)-Gauge Theory
The quantum properties of localized finite energy solutions to classical
Euler-Lagrange equations are investigated using the method of collective
coordinates. The perturbation theory in terms of inverse powers of the coupling
constant is constructed, taking into account the conservation laws of
momentum and angular momentum (invariance of the action with respect to the
group of motion M(3) of 3-dimensional Euclidean space) rigorously in every
order of perturbation theory.Comment: LaTex, 17 pages typos correcte
Topological Coherent Modes for Nonlinear Schr\"odinger Equation
Nonlinear Schr\"odinger equation, complemented by a confining potential,
possesses a discrete set of stationary solutions. These are called coherent
modes, since the nonlinear Schr\"odinger equation describes coherent states.
Such modes are also named topological because the solutions corresponding to
different spectral levels have principally different spatial dependences. The
theory of resonant excitation of these topological coherent modes is presented.
The method of multiscale averaging is employed in deriving the evolution
equations for resonant guiding centers. A rigorous qualitative analysis for
these nonlinear differential equations is given. Temporal behaviour of
fractional populations is illustrated by numerical solutions.Comment: 14 pages, Latex, no figure
The gravitational S-matrix
We investigate the hypothesized existence of an S-matrix for gravity, and
some of its expected general properties. We first discuss basic questions
regarding existence of such a matrix, including those of infrared divergences
and description of asymptotic states. Distinct scattering behavior occurs in
the Born, eikonal, and strong gravity regimes, and we describe aspects of both
the partial wave and momentum space amplitudes, and their analytic properties,
from these regimes. Classically the strong gravity region would be dominated by
formation of black holes, and we assume its unitary quantum dynamics is
described by corresponding resonances. Masslessness limits some powerful
methods and results that apply to massive theories, though a continuation path
implying crossing symmetry plausibly still exists. Physical properties of
gravity suggest nonpolynomial amplitudes, although crossing and causality
constrain (with modest assumptions) this nonpolynomial behavior, particularly
requiring a polynomial bound in complex s at fixed physical momentum transfer.
We explore the hypothesis that such behavior corresponds to a nonlocality
intrinsic to gravity, but consistent with unitarity, analyticity, crossing, and
causality.Comment: 46 pages, 10 figure
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