Path integral over reparametrizations: Lévy flights versus random walks

We investigate the properties of the path integral over reparametrizations (or the boundary value of the Liouville field in string theory). Discretizing the path integral, we apply the Metropolis–Hastings algorithm to numerical simulations of a proper (subordinator) stochastic process and find that typical trajectories are not Brownian but rather have discontinuities of the type of Lévy's flights. We study a fractal structure of these trajectories and show that their Hausdorff dimension is zero. We confirm thereby previous results on QCD scattering amplitudes by analytical and numerical calculations. We also perform Monte Carlo simulations of the path integral over reparametrization in the effective string ansatz for a circular Wilson loop and discuss their subtleties associated with the discretization of Douglas' functional.     

On the chiral anomaly in non-Riemannian spacetimes

Thetranslation Chern-Simons type three-formcoframe∧torsion on a Riemann-Cartan spacetime is related (by differentiation) to the Nieh-Yan fourform. Following Chandia and Zanelli, two spaces with nontrivial translational Chern-Simons forms are discussed. We then demonstrate, first within the classical Einstein-Cartan-Dirac theory and second in the quantum heat kernel approach to the Dirac operator, how the Nieh-Yan form surfaces in both contexts, in contrast to what has been assumed previously.     

Structure of liquid-vapor interface of square well fluid confined in a cylindrical pore

By means of the canonical Monte Carlo simulations, the vapor-liquid (VL) equilibrium and structure of square well (SW) fluids confined in a single cylindrical pore with repulsive surface, have been studied. Coexistence curves of the confined VL interface are determined for a wide range of temperatures and pore diameters. It is demonstrated that the confinement not only reduces the VL coexistence region but also induces strong inhomogeneities of the VL interface: coexistence liquid densities are different at the pore center and at the wall surface. It may be considered as a preliminary step for an isolated droplet formation inside the pore, as well as a tentative reason of the two VL phase transitions of simple fluids adsorbed into disordered porous media.     

Covering group and graph of discretized volumes

We consider a discretized volume V consisting of finite, congruent and attached copies of a tile t. We find a group L _V the orbit of which, when applied to t, is just V. We show the connection between the structural matrixQ in the formal solution of a boundary value problem formulated for volume V and the so called auxiliary matrix of the graph Γ _v associated with V. We show boundary value problems to be isomorphic if the graphs associated with the volumes are isomorphic, or, if the covering groups are Sunada pairs.     

Nonlinear BLOCH-wave interaction and bragg scattering in optically induced lattices

We study, both theoretically and experimentally, the Bragg scattering of light in optically induced photonic lattices and reveal the key physical mechanisms which govern the nonlinear self-action of narrow beams under the combined effects of Bragg scattering and wave diffraction, allowing for selecting bands with different effective dispersion.     

Complete band gaps in one-dimensional left-handed periodic structures

Artificially fabricated structures with periodically modulated parameters such as photonic crystals offer novel ways of controlling the flow of light due to the existence of a range of forbidden frequencies associated with a photonic band gap. It is believed that modulation of the refractive index in all three spatial dimensions is required to open a complete band gap and prevent the propagation of electromagnetic waves in all directions. Here we reveal that, in sharp contrast to what was known before and contrary to the accepted physical intuition, a one-dimensional periodic structure containing the layers of transparent left-handed (or negative-index) metamaterial can trap light in three-dimensional space due to the existence of a complete band gap.     

Multigap discrete vector solitons

We analyze nonlinear collective effects in periodic systems with multigap transmission spectra such as light in waveguide arrays or Bose-Einstein condensates in optical lattices. We reveal that the interband interactions in nonlinear periodic structures can be efficiently managed by controlling their geometry. We predict novel types of discrete vector solitons supported by nonlinear coupling between different band gaps and study their stability.     

Matter-wave gap solitons in atomic band-gap structures

We demonstrate that a Bose-Einstein condensate in an optical lattice forms a reconfigurable matter-wave structure with a band-gap spectrum, which resembles a nonlinear photonic crystal for light waves. We study in detail the case of a two-dimensional square optical lattice and show that this atomic band-gap structure allows nonlinear localization of atomic Bloch waves in the form of two-dimensional matter-wave gap solitons.     

Polarization multistability of cavity polaritons

New effects of polarization multistability and polarization hysteresis in a coherently driven polariton system in a semiconductor microcavity are predicted and theoretically analyzed. The multistability arises due to polarization-dependent polariton-polariton interactions and can be revealed in polarization resolved photoluminescence experiments. The pumping power required to observe this effect is 4 orders of magnitude lower than the characteristic pumping power in conventional bistable optical systems.     

D-scan measurement of nonlinear refractive index in fibers heavily doped with GeO2

Concentration dependence of nonlinear refractive index n2 in fibers heavily doped with GeO2 is studied by using the D-scan method. Good agreement with an empirical dependence established earlier with lower GeO2 concentrations by the cw dual-frequency beat signal technique is shown for GeO2 concentrations up to approximately 100 mol.%. The highest values of the nonlinear coefficient gamma at 1.25 microm of 47.9, 57.7, and 70.9 W(-1) km(-1) were obtained in fibers doped with 67, 75, and 97 mol.% GeO2, respectively.