A theory of thin shells with orbiting constituents

The self-gravitating, spherically symmetric thin shells built of orbiting particles are sstudied. Two new features are found. One is the minimal possible value for an angular momentum of particles, above which elleptic orbits become possible. The second is the coexistence of both the wormhole solutions and the elleptic or hyperbolic orbits for the same values of the parameters (but different initial conditions). Possible applications of these results to astrophysics and quantum black holes are briefly discussed.Comment: 22 pages, Latex, 10 eps figures. CERN preprint no. CERN-TH 2000-16

Vacuum decay via Lorentzian wormholes

We speculate about the spacetime description due to the presence of Lorentzian wormholes (handles in spacetime joining two distant regions or other universes) in quantum gravity. The semiclassical rate of production of these Lorentzian wormholes in Reissner-Nordstr\"om spacetimes is calculated as a result of the spontaneous decay of vacuum due to a real tunneling configuration. In the magnetic case it only depends on the field theoretical fine structure constant. We predict that the quantum probability corresponding to the nucleation of such geodesically complete spacetimes should be actually negligible in our physical Universe

Vacuum shell in the Schwarzschild-de Sitter world

We construct the classification scheme for all possible evolution scenarios and find the corresponding global geometries for dynamics of a thin spherical vacuum shell in the Schwarzschild-de Sitter metric. This configuration is suitable for the modelling of vacuum bubbles arising during cosmological phase transitions in the early Universe. The distinctive final types of evolution from the local point of view of a rather distant observer are either the unlimited expansion of the shell or its contraction with a formation of black hole (with a central singularity) or wormhole (with a baby universe in interior).Comment: 15 pages, 8 figure

Coherent States of the SU(N) groups

Coherent states $(CS)$ of the $SU(N)$ groups are constructed explicitly and their properties are investigated. They represent a nontrivial generalization of the spining $CS$ of the $SU(2)$ group. The $CS$ are parametrized by the points of the coset space, which is, in that particular case, the projective space $CP^{N-1}$ and plays the role of the phase space of a corresponding classical mechanics. The $CS$ possess of a minimum uncertainty, they minimize an invariant dispersion of the quadratic Casimir operator. The classical limit is ivestigated in terms of symbols of operators. The role of the Planck constant playes $h=P^{-1}$, where $P$ is the signature of the representation. The classical limit of the so called star commutator generates the Poisson bracket in the $CP^{N-1}$ phase space. The logarithm of the modulus of the $CS$ overlapping, being interpreted as a symmetric in the space, gives the Fubini-Study metric in $CP^{N-1}$. The $CS$ constructed are useful for the quasi-classical analysis of the quantum equations of the $SU(N)$ gauge symmetric theories.Comment: 19pg, IFUSP/P-974 March/199

Dynamics of a thin shell in the Reissner-Nordstrom metric

We describe the dynamics of a thin spherically symmetric gravitating shell in the Reissner-Nordstrom metric of the electrically charged black hole. The energy-momentum tensor of electrically neutral shell is modelled by the perfect fluid with a polytropic equation of state. The motion of a shell is described fully analytically in the particular case of the dust equation of state. We construct the Carter-Penrose diagrams for the global geometry of the eternal black hole, which illustrate all possible types of solutions for moving shell. It is shown that for some specific range of initial parameters there are possible the stable oscillating motion of the shell transferring it consecutively in infinite series of internal universes. We demonstrate also that this oscillating type of motion is possible for an arbitrary polytropic equation of state on the shell.Comment: 17 pages, 7 figure

Correlations in Systems of Complex Directed Macromolecules

An ensemble of directed macromolecules on a lattice is considered, where the constituting molecules are chosen as a random sequence of N different types. The same type of molecules experiences a hard-core (exclusion) interaction. We study the robustness of the macromolecules with respect to breaking and substituting individual molecules, using a 1/N expansion. The properties depend strongly on the density of macromolecules. In particular, the macromolecules are robust against breaking and substituting at high densities.Comment: 9 pages, 4 figure

On the Eigenvalue Density of Real and Complex Wishart Correlation Matrices

Wishart correlation matrices are the standard model for the statistical analysis of time series. The ensemble averaged eigenvalue density is of considerable practical and theoretical interest. For complex time series and correlation matrices, the eigenvalue density is known exactly. In the real case, however, a fundamental mathematical obstacle made it forbidingly complicated to obtain exact results. We use the supersymmetry method to fully circumvent this problem. We present an exact formula for the eigenvalue density in the real case in terms of twofold integrals and finite sums.Comment: 4 pages, 2 figure

On the Coherent State Path Integral for Linear Systems

We present a computation of the coherent state path integral for a generic linear system using ``functional methods'' (as opposed to discrete time approaches). The Gaussian phase space path integral is formally given by a determinant built from a first-order differential operator with coherent state boundary conditions. We show how this determinant can be expressed in terms of the symplectic transformation generated by the (in general, time-dependent) quadratic Hamiltonian for the system. We briefly discuss the conditions under which the coherent state path integral for a linear system actually exists. A necessary -- but not sufficient -- condition for existence of the path integral is that the symplectic transformation generated by the Hamiltonian is (unitarily) implementable on the Fock space for the system.Comment: 15 pages, plain Te

Flat World of Dilatonic Domain Walls

We study dilatonic domain walls specific to superstring theory. Along with the matter fields and metric the dilaton also changes its value in the wall background. We found supersymmetric (extreme) solutions which in general interpolate between isolated superstring vacua with non-equal value of the matter potential; they correspond to the static, planar domain walls with {\it flat} metric in the string (sigma model) frame. We point out similarities between the space-time of dilatonic walls and that of charged dilatonic black holes. We also comment on non-extreme solutions corresponding to expanding bubbles.Comment: 11 pgs (+2 figures available upon request), UPR-560-

Nonlinear modes for the Gross-Pitaevskii equation -- demonstrative computation approach

A method for the study of steady-state nonlinear modes for Gross-Pitaevskii equation (GPE) is described. It is based on exact statement about coding of the steady-state solutions of GPE which vanish as $x\to+\infty$ by reals. This allows to fulfill {\it demonstrative computation} of nonlinear modes of GPE i.e. the computation which allows to guarantee that {\it all} nonlinear modes within a given range of parameters have been found. The method has been applied to GPE with quadratic and double-well potential, for both, repulsive and attractive nonlinearities. The bifurcation diagrams of nonlinear modes in these cases are represented. The stability of these modes has been discussed.Comment: 21 pages, 6 figure