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