On the variational principle for dust shells in General Relativity

The variational principle for a thin dust shell in General Relativity is constructed. The principle is compatible with the boundary-value problem of the corresponding Euler-Lagrange equations, and leads to ``natural boundary conditions'' on the shell. These conditions and the gravitational field equations which follow from an initial variational principle, are used for elimination of the gravitational degrees of freedom. The transformation of the variational formula for spherically-symmetric systems leads to two natural variants of the effective action. One of these variants describes the shell from a stationary interior observer's point of view, another from the exterior one. The conditions of isometry of the exterior and interior faces of the shell lead to the momentum and Hamiltonian constraints. The canonical equivalence of the mentioned systems is shown in the extended phase space. Some particular cases are considered.Comment: 25 pages, RevTeX, no figures, revised version, typos corrected, accepted for publication in Journal of Mathematical Physic

Hopping magneto-transport via nonzero orbital momentum states and organic magnetoresistance

In hopping magnetoresistance of doped insulators, an applied magnetic field shrinks the electron (hole) s-wave function of a donor or an acceptor and this reduces the overlap between hopping sites resulting in the positive magnetoresistance quadratic in a weak magnetic field, B. We extend the theory of hopping magnetoresistance to states with nonzero orbital momenta. Different from s-states, a weak magnetic field expands the electron (hole) wave functions with positive magnetic quantum numbers, m > 0, and shrinks the states with negative m in a wide region outside the point defect. This together with a magnetic-field dependence of injection/ionization rates results in a negative weak-field magnetoresistance, which is linear in B when the orbital degeneracy is lifted. The theory provides a possible explanation of a large low-field magnetoresistance in disordered pi-conjugated organic materials (OMAR).Comment: 4 pages, 3 figure

On the nature of Bose-Einstein condensation enhanced by localization

In a previous paper we established that for the perfect Bose gas and the mean-field Bose gas with an external random or weak potential, whenever there is generalized Bose-Einstein condensation in the eigenstates of the single particle Hamiltonian, there is also generalized condensation in the kinetic energy states. In these cases Bose-Einstein condensation is produced or enhanced by the external potential. In the present paper we establish a criterion for the absence of condensation in single kinetic energy states and prove that this criterion is satisfied for a class of random potentials and weak potentials. This means that the condensate is spread over an infinite number of states with low kinetic energy without any of them being macroscopically occupied

A study of the impact of broken neutral in a distribution system

Abstract: In this paper a study of the impact of the neutral conductor in a distribution system is presented. The causes which determine faults of the neutral conductor together with its effects are presented. The paper proposes a solution which will minimize the impact of the neutral failure

Exactness of the Bogoliubov approximation in random external potentials

We investigate the validity of the Bogoliubov c-number approximation in the case of interacting Bose-gas in a \textit{homogeneous random} media. To take into account the possible occurence of type III generalized Bose-Einstein condensation (i.e. the occurrence of condensation in an infinitesimal band of low kinetic energy modes without macroscopic occupation of any of them) we generalize the c-number substitution procedure to this band of modes with low momentum. We show that, as in the case of the one-mode condensation for translation-invariant interacting systems, this procedure has no effect on the exact value of the pressure in the thermodynamic limit, assuming that the c-numbers are chosen according to a suitable variational principle. We then discuss the relation between these c-numbers and the (total) density of the condensate