One-Step Recurrences for Stationary Random Fields on the Sphere

Recurrences for positive definite functions in terms of the space dimension have been used in several fields of applications. Such recurrences typically relate to properties of the system of special functions characterizing the geometry of the underlying space. In the case of the sphere ${\mathbb S}^{d-1} \subset {\mathbb R}^d$ the (strict) positive definiteness of the zonal function $f(\cos \theta)$ is determined by the signs of the coefficients in the expansion of $f$ in terms of the Gegenbauer polynomials $\{C^\lambda_n\}$, with $\lambda=(d-2)/2$. Recent results show that classical differentiation and integration applied to $f$ have positive definiteness preserving properties in this context. However, in these results the space dimension changes in steps of two. This paper develops operators for zonal functions on the sphere which preserve (strict) positive definiteness while moving up and down in the ladder of dimensions by steps of one. These fractional operators are constructed to act appropriately on the Gegenbauer polynomials $\{C^\lambda_n\}$

Once again: Instanton method vs. WKB

A recent analytic test of the instanton method performed by comparing the exact spectrum of the Lam${\acute e}$ potential (derived from representations of a finite dimensional matrix expressed in terms of $su(2)$ generators) with the results of the tight--binding and instanton approximations as well as the standard WKB approximation is commented upon. It is pointed out that in the case of the Lam${\acute e}$ potential as well as others the WKB--related method of matched asymptotic expansions yields the exact instanton result as a result of boundary conditions imposed on wave functions which are matched in domains of overlap.Comment: 10 pages, no figures. References list revised according to JHE

Corrections to the thermodynamics of Schwarzschild-Tangherlini black hole and the generalized uncertainty principle

We investigate the thermodynamics of Schwarzschild-Tangherlini black hole in the context of the generalized uncertainty principle. The corrections to the Hawking temperature, entropy and the heat capacity are obtained via the modified Hamilton-Jacobi equation. These modifications show that the GUP changes the evolution of Schwarzschild-Tangherlini black hole. Specially, the GUP effect becomes susceptible when the radius or mass of black hole approach to the order of Planck scale, it stops radiating and leads to black hole remnant. Meanwhile, the Planck scale remnant can be confirmed through the analysis of the heat capacity. Those phenomenons imply that the GUP may give a way to solve the information paradox. Besides, we also investigate the possibilities to observe the black hole at LHC, the results demonstrate that the black hole can not be produced in the recent LHC.Comment: 12 pages, 6 figure

Enhanced flux pinning in YBa2Cu3O7-d films by nano-scaled substrate surface roughness

Nano-scaled substrate surface roughness is shown to strongly influence the critical current density Jc in YBCO films made by pulse-laser-deposition on the crystalline LaAlO3 substrates consisting of two separate twin-free and twin-rich regions. The nano-scaled corrugated surface was created in the twin-rich region during the deposition process. Using magneto-optical imaging techniques coupled with optical and atomic force microscopy, we observed an enhanced flux pinning in the YBCO films in the twin-rich region, resulted in \~30% increase in Jc, which was unambiguously confirmed by the direct transport measurement.Comment: 16 pages, 3 figures, accepted by Applied Physics Letter

Unconventional Planar Hall Effect in Exchange-Coupled Topological Insulator-Ferromagnetic Insulator Heterostructures

The Dirac electrons occupying the surface states (SSs) of topological insulators (TIs) have been predicted to exhibit many exciting magneto-transport phenomena. Here we report on the first experimental observation of an unconventional planar Hall effect (PHE) and an electrically gate-tunable hysteretic planar magnetoresistance (PMR) in EuS/TI heterostructures, in which EuS is a ferromagnetic insulator (FMI) with an in-plane magnetization. In such exchange-coupled FMI/TI heterostructures, we find a significant (suppressed) PHE when the in-plane magnetic field is parallel (perpendicular) to the electric current. This behavior differs from previous observations of the PHE in ferromagnets and semiconductors. Furthermore, as the thickness of the 3D TI films is reduced into the 2D limit, in which the Dirac SSs develop a hybridization gap, we find a suppression of the PHE around the charge neutral point indicating the vital role of Dirac SSs in this phenomenon. To explain our findings, we outline a symmetry argument that excludes linear-Hall mechanisms and suggest two possible non-linear Hall mechanisms that can account for all the essential qualitative features in our observations.Comment: 17 pages, 4 figures, accepted by Phys. Rev.

Measure representation and multifractal analysis of complete genomes

This paper introduces the notion of measure representation of DNA sequences. Spectral analysis and multifractal analysis are then performed on the measure representations of a large number of complete genomes. The main aim of this paper is to discuss the multifractal property of the measure representation and the classification of bacteria. From the measure representations and the values of the $D_{q}$ spectra and related $C_{q}$ curves, it is concluded that these complete genomes are not random sequences. In fact, spectral analyses performed indicate that these measure representations considered as time series, exhibit strong long-range correlation. For substrings with length K=8, the $D_{q}$ spectra of all organisms studied are multifractal-like and sufficiently smooth for the $C_{q}$ curves to be meaningful. The $C_{q}$ curves of all bacteria resemble a classical phase transition at a critical point. But the 'analogous' phase transitions of chromosomes of non-bacteria organisms are different. Apart from Chromosome 1 of {\it C. elegans}, they exhibit the shape of double-peaked specific heat function.Comment: 12 pages with 9 figures and 1 tabl

Bulge formation from SSCs in a responding cuspy dark matter halo

We simulate the bulge formation in very late-type dwarf galaxies from circumnuclear super star clusters (SSCs) moving in a responding cuspy dark matter halo (DMH). The simulations show that (1) the response of DMH to sinking of SSCs is detectable only in the region interior to about 200 pc. The mean logarithmic slope of the responding DM density profile over that area displays two different phases: the very early descent followed by ascent till approaching to 1.2 at the age of 2 Gyrs. (2) the detectable feedbacks of the DMH response on the bulge formation turned out to be very small, in the sense that the formed bulges and their paired nuclear cusps in the fixed and the responding DMH are basically the same, both are consistent with $HST$ observations. (3) the yielded mass correlation of bulges to their nuclear (stellar) cusps and the time evolution of cusps' mass are accordance with recent findings on relevant relations. In combination with the consistent effective radii of nuclear cusps with observed quantities of nuclear clusters, we believe that the bulge formation scenario that we proposed could be a very promising mechanism to form nuclear clusters.Comment: 27 pages, 11 figures, accepted for publication in Ap