Abelian Higgs model with a Chern-Simons term in 3-dimensional gravitation

We consider the Abelian Higgs model with a Chern-Simons term coupled to the Einstein theory of gravitation in 3-dimensional space-time. We seek a finite solution, regular everywhere, having a stationary, cylindrically symmetric metric. We analyze these field equations and we suggest that such a solution exists. We find that the asymptotic metric of this solution corresponds to that which describes gravitationally a massive particle with spin. We obtain explicitly the expression of the spin. We give only the expression of the mass in the first order with respect to the gravitational coupling constant.     

Hermite Polynomial Representation of the Spin States

We construct the invertible map of the spin-state density operator onto the quasiprobability distribution of three continuous variables. We discuss the connection of this map with two-mode electromagnetic-field oscillators. We give the inversion formula for the spin-density matrix in terms of the Hermite polynomials. We examine the connection of the map constructed with the spin-tomographic representation. We consider the problem of the magnetic-moment rotation in the magnetic field in the suggested representation of spin states.     

Josephson pancakes in layered superconductors

We consider a pancake vortex in a layered superconductor with linear defects in the superconducting planes. We treat these defects as Josephson junctions. We show that the tunneling Josephson current through these junctions results in a pancake with a superconducting core. We find the mobility of a Josephson pancake.     

Cohomological obstructions to the equivariant extension of closed invariant forms

We study under what condition a closed invariant form on a manifold with a group action admits an equivariant extension. We derive a sequence of obstructions in the cohomology groups of the Lie algebra with coefficients in appropriate modules. We illustrate the result with two specific examples. We then discuss when such cohomological obstructions vanish. Finally, we compare our analysis with the spectral sequence point of view.     

Simulations of the Hubbard model

We discuss results of simulations of the Hubbard model of interacting electrons on a lattice. We start with a brief discussion of methodology and point out some of the outstanding problems. We then discuss results of simulations of the model in three, two, and one dimension, particularly in connection with its magnetic and superconducting properties. We conclude with a brief discussion of future directions.     

Optical vortex solitons and soliton clusters in photonic crystal fibres

We study higher-order nonlinear modes in the form of vortex solitons and soliton clusters propagating in the waveguides created in photonic crystal fibers made of a material with the focusing Kerr nonlinearity. We find numerically different families of such nonlinear modes with a nontrivial topology and study their bifurcations. We also study the soliton stability to propagation. We demonstrate that waveguides in photonic crystal fibers may support a variety of soliton clusters with the symmetries that may differ from the lattice symmetry. We also discuss briefly the case of a dual-core coupler created by two neighboring cores in a photonic crystal fiber and find numerically the profiles of symmetric and asymmetric nonlinear modes.     

Numerical modeling of the propagation of electromagnetic radiation in 3D photonic crystals

We describe the mathematical model and program BAL 3D that enables one to solve numerically three-dimensional Maxwell equations in inhomogeneous media. We present the results of calculations of the electromagnetic-radiation propagation in a 3D quasiperiodic medium (photonic crystal). We found the positions of stop bands in photonic crystals and calculate the reflection coefficients for composite materials consisting of artificial opals with pores filled with water. We compare our results with the experimental data.     

Classical Mechanics in Hilbert Space,Part 2

We continue from Part 1. We will illustrate the general theory of Hamiltonian mechanics in the Lie group formalism. We then obtain the Hamiltonian formalism in the Hilbert spaces of square integrable functions on the symplectic spaces. We illustrate this general theory with several concrete examples, two of which are the representations of the Lorentz group and the Poincaré group with interactions.     

Atomic absorbers for controlling pulse propagation in resonators

We consider pulse propagation through a Fabry-Perot cavity with silver mirrors that contain macroscopic samples of resonant absorbers. We show that the pulse velocity can be tuned from subluminal to superluminal in a strongly coupled atom-cavity system. We delineate the effects of the interplay of cavity and absorbers. We demonstrate the saturation effects of pulse advancement with increasing mirror thickness and atomic damping.     

Topological states at exceptional points

We consider an N-level non-Hermitian Hamiltonian with an exceptional point of order N. We define adiabatic equivalence in such systems and explore topological phase. We show that the topological exceptional states appear at the interface of topologically distinct systems. We discuss that topological states appear even in closed systems. We explore dynamical robustness of exceptional edge states.     

Non-stationary effects in the coupled quantum dots influenced by the electron-phonon interaction

We analyzed time evolution of the localized charge in the system of two interacting single level quantum dots coupled with the continuous spectrum states in the presence of electron-phonon interaction. We demonstrated that electron-phonon interaction leads to an increase in localized charge relaxation rate. We also found that several time scales with different relaxation rates appear in the system in the case of non-resonant tunneling between the dots. We revealed the formation of oscillations in the filling numbers time evolution caused by the emission and adsorption processes of phonons.     

Flapping states of a flag in an inviscid fluid: bistability and the transition to chaos

We investigate the "flapping flag" instability through a model for an inextensible flexible sheet in an inviscid 2D flow with a free vortex sheet. We solve the fully-nonlinear dynamics numerically and find a transition from a power spectrum dominated by discrete frequencies to an apparently continuous spectrum of frequencies. We compute the linear stability domain which agrees with previous approximate models in scaling but differs by large multiplicative factors. We also find hysteresis, in agreement with previous experiments.     

Superfluid phases of the three-species fermion gas

We discuss the zero temperature phase diagram of a dilute gas with three fermionic species. We make use of solvable limits to conjecture the behavior of the system in the “unitary” regions. The physics of the Thomas-Efimov effect plays a role in these considerations. We find a rich phase diagram with superfluid, gapless superfluid and inhomogeneous phases with different symmetry breaking patterns. We then discuss one particular possible experimental implementation in a system of ⁶Li atoms and the possible phases arising in this system as an external magnetic field is varied across three overlapping Feshbach resonances. We also suggest how to experimentally distinguish the different phases.     

Non-abelian eikonal exponentiation

Recently, Gatheral [1] has generalized the well-known exponentiation properties of soft photons in QED to the case of soft gluons in QCD in the eikonal approximation. We add three things to his work. (i) We clarify the definition of the colour weight factors which appear in the exponent. (ii) We show how the eikonal approximation can be renormalized, consistently with the exponentiation. (iii) We derive a differential equation obeyed by the cross section for emission of soft gluons with given maximum total energy. We also discuss the relationship between the exponentiation theorem and expectation values of Wilson loops.     

Statistical physics in deformed spaces with minimal length

We considered the thermodynamics in spaces with deformed commutation relations leading to the existence of minimal length. We developed a classical method of the partition function evaluation. We calculated the partition function and heat capacity for ideal gas and harmonic oscillators using this method. The obtained results are in good agreement with the exact quantum ones. We also showed that the minimal length introduction reduces degrees of freedom of an arbitrary system in the high temperature limit significantly.     

Mapping electromagnetic fields near a subwavelength hole

We study, both experimentally and theoretically, the scattering of electromagnetic waves by a subwavelength hole fabricated in a thin metallic film. We employ the scanning near-field optical microscopy in order to reconstruct experimentally the full three-dimensional structure of the electromagnetic fields in the vicinity of the hole. We observe an interference of all excited waves with an incident laser beam which allows us to gain the information about the wave phases. Along with the well-known surface plasmon polaritons propagating primarily in the direction of the incident beam polarization, we observe the free-space radiation diffracted by the hole. We compare the experimental results with the fields of pure electric and pure magnetic dipoles as well as with direct numerical simulations. We confirm that a single hole in a thin metallic film excited at the normal incidence manifests itself as an effective magnetic dipole in the visible spectral range.     

A General Framework for Localization of Classical Waves: I. Inhomogeneous Media and Defect Eigenmodes

We introduce a general framework for studying the localization of classical waves in inhomogeneous media, which encompasses acoustic waves with position dependent compressibility and mass density, elastic waves with position dependent Lamé moduli and mass density, and electromagnetic waves with position dependent magnetic permeability and dielectric constant. We also allow for anisotropy. We develop mathematical methods to study wave localization in inhomogeneous media. We show localization for local perturbations (defects) of media with a spectral gap, and study midgap eigenmodes.     

Relativistic many body approach for unstable nuclei and supernova

We study the properties of unstable nuclei and the equations of state of nuclear matter in the framework of the relativistic many body theory. We take the relativistic mean field (RMF) theory as a phenomenological theory with several parameters, whose form is constrained by the successful microscopic theory (RBHF), and whose values are extracted by using the experimental values of unstable nuclei. We find the outcome with the newly obtained parameter set (TMA) is promising in comparison with various experimental data. We study also the neutron star profiles with the equation of state of nuclear matter with the use of TMA.     

On the propagation of a fissioning system across the barrier towards scission

We describe the motion of a fissioning nuclear system from the potential minimum across the saddle region to scission by means of a Fokker-Planck type equation. We pay particular attention to the problems associated with the motion of broad distributions in phase space. We introduce propagators to obtain global solutions. The results are compared with Kramers' stationary solution for all friction and with simplified dynamical calculations which start behind or on top of the barriers. We are able to find stationary solutions numerically for all finite friction values. We compare the corresponding decay rates with Kramers' formulae for large and small friction.     

Reliable and economical method to join optical tables

We present a practical method for joining pneumatically floated optical tables with no manufacturer preparation. We compare the stability of the joined table with one of its parts alone using Michelson Interferometry. We also compare the stability of two different pneumatic leg configurations in order to find the optimal one. We demonstrate that the joined table has comparable rigidity to its segments.