Escaping the crunch: gravitational effects in classical transitions

During eternal inflation, a landscape of vacua can be populated by the nucleation of bubbles. These bubbles inevitably collide, and collisions sometimes displace the field into a new minimum in a process known as a classical transition. In this paper, we examine some new features of classical transitions that arise when gravitational effects are included. Using the junction condition formalism, we study the conditions for energy conservation in detail, and solve explicitly for the types of allowed classical transition geometries. We show that the repulsive nature of domain walls, and the de Sitter expansion associated with a positive energy minimum, can allow for classical transitions to vacua of higher energy than that of the colliding bubbles. Transitions can be made out of negative or zero energy (terminal) vacua to a de Sitter phase, re-starting eternal inflation, and populating new vacua. However, the classical transition cannot produce vacua with energy higher than the original parent vacuum, which agrees with previous results on the construction of pockets of false vacuum. We briefly comment on the possible implications of these results for various measure proposals in eternal inflation.Comment: 21 pages, 10 figure

Influence of Homeotropic Anchoring Walls upon Nematic and Smectic Phases

McMillan liquid crystal model sandwiched between strong homeotropic anchoring walls is studied. Phase transitions between isotropic, nematic, and smectic A phases are investigated for wide ranges of an interaction parameter and of the system thickness. It is confirmed that the anchoring walls induce an increase in transition temperatures, dissappearance of phase transitions, and an appearance of non-spontaneous nematic phase. The similarity between influence of anchoring walls and that of external fields is discussed.Comment: 5 pages, 6 figure

Representations of hom-Lie algebras

In this paper, we study representations of hom-Lie algebras. In particular, the adjoint representation and the trivial representation of hom-Lie algebras are studied in detail. Derivations, deformations, central extensions and derivation extensions of hom-Lie algebras are also studied as an application.Comment: 16 pages, multiplicative and regular hom-Lie algebras are used, Algebra and Representation Theory, 15 (6) (2012), 1081-109

Effective Dielectric Tensor for Electromagnetic Wave Propagation in Random Media

We derive exact strong-contrast expansions for the effective dielectric tensor \epeff of electromagnetic waves propagating in a two-phase composite random medium with isotropic components explicitly in terms of certain integrals over the $n$-point correlation functions of the medium. Our focus is the long-wavelength regime, i.e., when the wavelength is much larger than the scale of inhomogeneities in the medium. Lower-order truncations of these expansions lead to approximations for the effective dielectric constant that depend upon whether the medium is below or above the percolation threshold. In particular, we apply two- and three-point approximations for \epeff to a variety of different three-dimensional model microstructures, including dispersions of hard spheres, hard oriented spheroids and fully penetrable spheres as well as Debye random media, the random checkerboard, and power-law-correlated materials. We demonstrate the importance of employing $n$-point correlation functions of order higher than two for high dielectric-phase-contrast ratio. We show that disorder in the microstructure results in an imaginary component of the effective dielectric tensor that is directly related to the {\it coarseness} of the composite, i.e., local volume-fraction fluctuations for infinitely large windows. The source of this imaginary component is the attenuation of the coherent homogenized wave due to scattering. We also remark on whether there is such attenuation in the case of a two-phase medium with a quasiperiodic structure.Comment: 40 pages, 13 figure

Absence of correlation between built-in electric dipole moment and quantum Stark effect in InAs/GaAs self-assembled quantum dots

We report significant deviations from the usual quadratic dependence of the ground state interband transition energy on applied electric fields in InAs/GaAs self-assembled quantum dots. In particular, we show that conventional second-order perturbation theory fails to correctly describe the Stark shift for electric field below $F = 10$ kV/cm in high dots. Eight-band ${\bf k}\cdot{\bf p}$ calculations demonstrate this effect is predominantly due to the three-dimensional strain field distribution which for various dot shapes and stoichiometric compositions drastically affects the hole ground state. Our conclusions are supported by two independent experiments.Comment: 4 pages, 4 figure

Effects of polarization on the transmission and localization of classical waves in weakly scattering metamaterials

We summarize the results of our comprehensive analytical and numerical studies of the effects of polarization on the Anderson localization of classical waves in one-dimensional random stacks. We consider homogeneous stacks composed entirely of normal materials or metamaterials, and also mixed stacks composed of alternating layers of a normal material and metamaterial. We extend the theoretical study developed earlier for the case of normal incidence [A. A. Asatryan et al, Phys. Rev. B 81, 075124 (2010)] to the case of off-axis incidence. For the general case where both the refractive indices and layer thicknesses are random, we obtain the long-wave and short-wave asymptotics of the localization length over a wide range of incidence angles (including the Brewster ``anomaly'' angle). At the Brewster angle, we show that the long-wave localization length is proportional to the square of the wavelength, as for the case of normal incidence, but with a proportionality coefficient substantially larger than that for normal incidence. In mixed stacks with only refractive-index disorder, we demonstrate that p-polarized waves are strongly localized, while for s-polarization the localization is substantially suppressed, as in the case of normal incidence. In the case of only thickness disorder, we study also the transition from localization to delocalization at the Brewster angle.Comment: 15 pages, 11 figures, accepted for publication in PR

Anomalous quantum confined Stark effects in stacked InAs/GaAs self-assembled quantum dots

Vertically stacked and coupled InAs/GaAs self-assembled quantum dots (SADs) are predicted to exhibit a strong non-parabolic dependence of the interband transition energy on the electric field, which is not encountered in single SAD structures nor in other types of quantum structures. Our study based on an eight-band strain-dependent ${\bf k}\cdot{\bf p}$ Hamiltonian indicates that this anomalous quantum confined Stark effect is caused by the three-dimensional strain field distribution which influences drastically the hole states in the stacked SAD structures.Comment: 4 pages, 4 figure

Spectral Dependence of Coherent Backscattering of Light in a Narrow-Resonance Atomic System

We report a combined theoretical and experimental study of the spectral and polarization dependence of near resonant radiation coherently backscattered from an ultracold gas of 85Rb atoms. Measurements in an approximately 6 MHz range about the 5s^{2}S_{1/2}- 5p^{2}P_{3/2}, F=3 - F'=4 hyperfine transition are compared with simulations based on a realistic model of the experimental atomic density distribution. In the simulations, the influence of heating of the atoms in the vapor, magnetization of the vapor, finite spectral bandwidth, and other nonresonant hyperfine transitions are considered. Good agreement is found between the simulations and measurements.Comment: 10 pages, 12 figur

Leibniz 2-algebras and twisted Courant algebroids

In this paper, we give the categorification of Leibniz algebras, which is equivalent to 2-term sh Leibniz algebras. They reveal the algebraic structure of omni-Lie 2-algebras introduced in \cite{omniLie2} as well as twisted Courant algebroids by closed 4-forms introduced in \cite{4form}. We also prove that Dirac structures of twisted Courant algebroids give rise to 2-term $L_\infty$-algebras and geometric structures behind them are exactly $H$-twisted Lie algebroids introduced in \cite{Grutzmann}.Comment: 22 pages, to appear in Comm. Algebr

Negative Magnetoresistance in the Nearest-neighbor Hopping Conduction

We propose a size effect which leads to the negative magnetoresistance in granular metal-insulator materials in which the hopping between two nearest neighbor clusters is the main transport mechanism. We show that the hopping probability increases with magnetic field. This is originated from the level crossing in a few-electron cluster. Thus, the overlap of electronic states of two neighboring clusters increases, and the negative magnetoresistance is resulted.Comment: Latex file, no figur