Modular symmetry and temperature flow of conductivities in quantum Hall systems with varying Zeeman energy

The behaviour of the critical point between quantum Hall plateaux, as the Zeeman energy is varied, is analysed using modular symmetry of the Hall conductivities following from the law of corresponding states. Flow diagrams for the conductivities as a function of temperature, with the magnetic field fixed, are constructed for different Zeeman energies, for samples with particle-hole symmetry.Comment: 15 pages, 13 figure

Measurement of the LCG2 and glite file catalogue's performance

When the Large Hadron Collider (LHC) begins operation at CERN in 2007 it will produce data in volumes never before seen. Physicists around the world will manage, distribute and analyse petabytes of this data using the middleware provided by the LHC Computing Grid. One of the critical factors in the smooth running of this system is the performance of the file catalogues which allow users to access their files with a logical filename without knowing their physical location. This paper presents a detailed study comparing the performance and respective merits and shortcomings of two of the main catalogues: the LCG File Catalogue and the gLite FiReMan catalogue

On the relation between p-adic and ordinary strings

The amplitudes for the tree-level scattering of the open string tachyons, generalised to the field of p-adic numbers, define the p-adic string theory. There is empirical evidence of its relation to the ordinary string theory in the p_to_1 limit. We revisit this limit from a worldsheet perspective and argue that it is naturally thought of as a continuum limit in the sense of the renormalisation group.Comment: 13 pages harvmac (b), 2 eps figures; v2: revtex, shortened, published versio

Non-vanishing of LL-functions associated to cusp forms of half-integral weight

In this article, we prove non-vanishing results for $L$-functions associated to holomorphic cusp forms of half-integral weight on average (over an orthogonal basis of Hecke eigenforms). This extends a result of W. Kohnen to forms of half-integral weight.Comment: 8 pages, Accepted for publication in Oman conference proceedings (Springer

The p-rank stratification on the Siegel moduli space with Iwahori level structure

Our concern in this paper is to describe the p-rank statification on the Siegel moduli space with Iwahori level structure over fields of positive characteristic. We calculate the dimension of the strata and describe the closure of a given stratum in terms of p-rank strata. We also examine the relationship between the p-rank stratification and the Kottwitz-Rapoport stratification.Comment: 29 pages; v2: new result Theorem 0.2 (2c), revised section 3; v3: Added formula for number of top-dimensional KR strata v4: simplified formula and corrected mistakes of v

Exact Superpotentials from Matrix Models

Dijkgraaf and Vafa (DV) have conjectured that the exact superpotential for a large class of N=1 SUSY gauge theories can be extracted from the planar limit of a certain holomorphic matrix integral. We test their proposal against existing knowledge for a family of deformations of N=4 SUSY Yang-Mills theory involving an arbitrary polynomial superpotential for one of the three adjoint chiral superfields. Specifically, we compare the DV prediction for these models with earlier results based on the connection between SUSY gauge theories and integrable systems. We find complete agreement between the two approaches. In particular we show how the DV proposal allows the extraction of the exact eigenvalues of the adjoint scalar in the confining vacuum and hence computes all related condensates of the finite-N gauge theory. We extend these results to include Leigh-Strassler deformations of the N=4 theory.Comment: 28 pages, 1 figure, latex with JHEP.cls, replaced with typos corrected and one clarifying commen

Factorizing Numbers with the Gauss Sum Technique: NMR Implementations

Several physics-based algorithms for factorizing large number were recently published. A notable recent one by Schleich et al. uses Gauss sums for distinguishing between factors and non-factors. We demonstrate two NMR techniques that evaluate Gauss sums and thus implement their algorithm. The first one is based on differential excitation of a single spin magnetization by a cascade of RF pulses. The second method is based on spatial averaging and selective refocusing of magnetization for Gauss sums corresponding to factors. All factors of 16637 and 52882363 are successfully obtained.Comment: 4 pages, 4 figures; Abstract and Conclusion are slightly modified. References added and formatted with Bibte

Integral representations of q-analogues of the Hurwitz zeta function

Two integral representations of q-analogues of the Hurwitz zeta function are established. Each integral representation allows us to obtain an analytic continuation including also a full description of poles and special values at non-positive integers of the q-analogue of the Hurwitz zeta function, and to study the classical limit of this q-analogue. All the discussion developed here is entirely different from the previous work in [4]Comment: 14 page