On topological bias of discrete sources in the gas of wormholes

The model of space in the form of a static gas of wormholes is considered. It is shown that the scattering on such a gas gives rise to the formation of a specific diffuse halo around every discrete source. Properties of the halo are determined by the distribution of wormholes in space and the halo has to be correlated with the distribution of dark matter. This allows to explain the absence of dark matter in intergalactic gas clouds. Numerical estimates for parameters of the gas of wormholes are also obtained

Entanglement in Valence-Bond-Solid States

This article reviews the quantum entanglement in Valence-Bond-Solid (VBS) states defined on a lattice or a graph. The subject is presented in a self-contained and pedagogical way. The VBS state was first introduced in the celebrated paper by I. Affleck, T. Kennedy, E. H. Lieb and H. Tasaki (abbreviation AKLT is widely used). It became essential in condensed matter physics and quantum information (measurement-based quantum computation). Many publications have been devoted to the subject. Recently entanglement was studied in the VBS state. In this review we start with the definition of a general AKLT spin chain and the construction of VBS ground state. In order to study entanglement, a block subsystem is introduced and described by the density matrix. Density matrices of 1-dimensional models are diagonalized and the entanglement entropies (the von Neumann entropy and Renyi entropy) are calculated. In the large block limit, the entropies also approach finite limits. Study of the spectrum of the density matrix led to the discovery that the density matrix is proportional to a projector.Comment: Published version, 80 pages, 8 figures; references update

Analytical Form of the Deuteron Wave Function Calculated within the Dispersion Approach

We present a convenient analytical parametrization of the deuteron wave function calculated within dispersion approach as a discrete superposition of Yukawa-type functions, in both configuration and momentum spaces.Comment: 3 pages, 2 figure; several minor corrections adde

Realization of compact Lie algebras in K\"ahler manifolds

The Berezin quantization on a simply connected homogeneous K\"{a}hler manifold, which is considered as a phase space for a dynamical system, enables a description of the quantal system in a (finite-dimensional) Hilbert space of holomorphic functions corresponding to generalized coherent states. The Lie algebra associated with the manifold symmetry group is given in terms of first-order differential operators. In the classical theory, the Lie algebra is represented by the momentum maps which are functions on the manifold, and the Lie product is the Poisson bracket given by the K\"{a}hler structure. The K\"{a}hler potentials are constructed for the manifolds related to all compact semi-simple Lie groups. The complex coordinates are introduced by means of the Borel method. The K\"{a}hler structure is obtained explicitly for any unitary group representation. The cocycle functions for the Lie algebra and the Killing vector fields on the manifold are also obtained

Combinatorics of BB-orbits and Bruhat--Chevalley order on involutions

Let $B$ be the group of invertible upper-triangular complex $n\times n$ matrices, $\mathfrak{u}$ the space of upper-triangular complex matrices with zeroes on the diagonal and $\mathfrak{u}^*$ its dual space. The group $B$ acts on $\mathfrak{u}^*$ by $(g.f)(x)=f(gxg^{-1})$, $g\in B$, $f\in\mathfrak{u}^*$, $x\in\mathfrak{u}$. To each involution $\sigma$ in $S_n$, the symmetric group on $n$ letters, one can assign the $B$-orbit $\Omega_{\sigma}\in\mathfrak{u}^*$. We present a combinatorial description of the partial order on the set of involutions induced by the orbit closures. The answer is given in terms of rook placements and is dual to A. Melnikov's results on $B$-orbits on $\mathfrak{u}$. Using results of F. Incitti, we also prove that this partial order coincides with the restriction of the Bruhat--Chevalley order to the set of involutions.Comment: 27 page

Quasi-Isotropization of the Inhomogeneous Mixmaster Universe Induced by an Inflationary Process

We derive a ``generic'' inhomogeneous ``bridge'' solution for a cosmological model in the presence of a real self-interacting scalar field. This solution connects a Kasner-like regime to an inflationary stage of evolution and therefore provides a dynamical mechanism for the quasi-isotropization of the universe. In the framework of a standard Arnowitt-Deser-Misner Hamiltonian formulation of the dynamics and by adopting Misner-Chitr\`e-like variables, we integrate the Einstein-Hamilton-Jacobi equation corresponding to a ``generic'' inhomogeneous cosmological model whose evolution is influenced by the coupling with a bosonic field, expected to be responsible for a spontaneous symmetry breaking configuration. The dependence of the detailed evolution of the universe on the initial conditions is then appropriately characterized.Comment: 17 pages, no figure, to appear on PR

Exceptional Points in a Microwave Billiard with Time-Reversal Invariance Violation

We report on the experimental study of an exceptional point (EP) in a dissipative microwave billiard with induced time-reversal invariance (T) violation. The associated two-state Hamiltonian is non-Hermitian and non-symmetric. It is determined experimentally on a narrow grid in a parameter plane around the EP. At the EP the size of T violation is given by the relative phase of the eigenvector components. The eigenvectors are adiabatically transported around the EP, whereupon they gather geometric phases and in addition geometric amplitudes different from unity

Boundary bound states and boundary bootstrap in the sine-Gordon model with Dirichlet boundary conditions.

We present a complete study of boundary bound states and related boundary S-matrices for the sine-Gordon model with Dirichlet boundary conditions. Our approach is based partly on the bootstrap procedure, and partly on the explicit solution of the inhomogeneous XXZ model with boundary magnetic field and of the boundary Thirring model. We identify boundary bound states with new ``boundary strings'' in the Bethe ansatz. The boundary energy is also computed.Comment: 25 pages, harvmac macros Report USC-95-001

The XXZ model with anti-periodic twisted boundary conditions

We derive functional equations for the eigenvalues of the XXZ model subject to anti-diagonal twisted boundary conditions by means of fusion of transfer matrices and by Sklyanin's method of separation of variables. Our findings coincide with those obtained using Baxter's method and are compared to the recent solution of Galleas. As an application we study the finite size scaling of the ground state energy of the model in the critical regime.Comment: 22 pages and 3 figure

Versal deformations of a Dirac type differential operator

If we are given a smooth differential operator in the variable $x\in {\mathbb R}/2\pi {\mathbb Z},$ its normal form, as is well known, is the simplest form obtainable by means of the \mbox{Diff}(S^1)-group action on the space of all such operators. A versal deformation of this operator is a normal form for some parametric infinitesimal family including the operator. Our study is devoted to analysis of versal deformations of a Dirac type differential operator using the theory of induced \mbox{Diff}(S^1)-actions endowed with centrally extended Lie-Poisson brackets. After constructing a general expression for tranversal deformations of a Dirac type differential operator, we interpret it via the Lie-algebraic theory of induced \mbox{Diff}(S^1)-actions on a special Poisson manifold and determine its generic moment mapping. Using a Marsden-Weinstein reduction with respect to certain Casimir generated distributions, we describe a wide class of versally deformed Dirac type differential operators depending on complex parameters