Gaussian fields and Gaussian sheets with generalized Cauchy covariance structure

Two types of Gaussian processes, namely the Gaussian field with generalized Cauchy covariance (GFGCC) and the Gaussian sheet with generalized Cauchy covariance (GSGCC) are considered. Some of the basic properties and the asymptotic properties of the spectral densities of these random fields are studied. The associated self-similar random fields obtained by applying the Lamperti transformation to GFGCC and GSGCC are studied.Comment: 32 pages, 6 figure

Majorana Fermions and Non-Abelian Statistics in Three Dimensions

We show that three dimensional superconductors, described within a Bogoliubov de Gennes framework can have zero energy bound states associated with pointlike topological defects. The Majorana fermions associated with these modes have non-Abelian exchange statistics, despite the fact that the braid group is trivial in three dimensions. This can occur because the defects are associated with an orientation that can undergo topologically nontrivial rotations. A new feature of three dimensional systems is that there are "braidless" operations in which it is possible to manipulate the groundstate associated with a set of defects without moving or measuring them. To illustrate these effects we analyze specific architectures involving topological insulators and superconductors.Comment: 4 pages, 2 figures, published versio

Effective response theory for zero energy Majorana bound states in three spatial dimensions

We propose a gravitational response theory for point defects (hedgehogs) binding Majorana zero modes in (3+1)-dimensional superconductors. Starting in 4+1 dimensions, where the point defect is extended into a line, a coupling of the bulk defect texture with the gravitational field is introduced. Diffeomorphism invariance then leads to an $SU(2)_2$ Kac-Moody current running along the defect line. The $SU(2)_2$ Kac-Moody algebra accounts for the non-Abelian nature of the zero modes in 3+1 dimensions. It is then shown to also encode the angular momentum density which permeates throughout the bulk between hedgehog-anti-hedgehog pairs.Comment: 7 pages, 3 figure

Finite Temperature Casimir Effect and Dispersion in the Presence of Compactified Extra Dimensions

Finite temperature Casimir theory of the Dirichlet scalar field is developed, assuming that there is a conventional Casimir setup in physical space with two infinitely large plates separated by a gap R and in addition an arbitrary number q of extra compacified dimensions. As a generalization of earlier theory, we assume in the first part of the paper that there is a scalar 'refractive index' N filling the whole of the physical space region. After presenting general expressions for free energy and Casimir forces we focus on the low temperature case, as this is of main physical interest both for force measurements and also for issues related to entropy and the Nernst theorem. Thereafter, in the second part we analyze dispersive properties, assuming for simplicity q=1, by taking into account dispersion associated with the first Matsubara frequency only. The medium-induced contribution to the free energy, and pressure, is calculated at low temperatures.Comment: 25 pages, one figure. Minor changes in the discussion. Version to appear in Physica Script

Modeling Single-File Diffusion by Step Fractional Brownian Motion and Generalized Fractional Langevin Equation

Single-file diffusion behaves as normal diffusion at small time and as anomalous subdiffusion at large time. These properties can be described by fractional Brownian motion with variable Hurst exponent or multifractional Brownian motion. We introduce a new stochastic process called Riemann-Liouville step fractional Brownian motion which can be regarded as a special case of multifractional Brownian motion with step function type of Hurst exponent tailored for single-file diffusion. Such a step fractional Brownian motion can be obtained as solution of fractional Langevin equation with zero damping. Various types of fractional Langevin equations and their generalizations are then considered to decide whether their solutions provide the correct description of the long and short time behaviors of single-file diffusion. The cases where dissipative memory kernel is a Dirac delta function, a power-law function, and a combination of both of these functions, are studied in detail. In addition to the case where the short time behavior of single-file diffusion behaves as normal diffusion, we also consider the possibility of the process that begins as ballistic motion.Comment: 12 pages, 7 figure

Finite Temperature Casimir Effect in Randall-Sundrum Models

The finite temperature Casimir effect for a scalar field in the bulk region of the two Randall-Sundrum models, RSI and RSII, is studied. We calculate the Casimir energy and the Casimir force for two parallel plates with separation $a$ on the visible brane in the RSI model. High-temperature and low-temperature cases are covered. Attractiveness versus repulsiveness of the temperature correction to the force is discussed in the typical special cases of Dirichlet-Dirichlet, Neumann-Neumann, and Dirichlet-Neumann boundary conditions at low temperature. The Abel-Plana summation formula is made use of, as this turns out to be most convenient. Some comments are made on the related contemporary literature.Comment: 33 pages latex, 2 figures. Some changes in the discussion. To appear in New J. Phy