119118347
On Casimir's Ghost

Abstract:We define on the universal enveloping superalgebra of 
$ a nonstandard adjoint action, endowing it with a module structure. This allows, in particular, to construct a bosonic operator which anticommutes with all the fermionic generators and which appears to be the square root of a certain Casimir operator.
115160247
Another derivation of the geometrical KPZ relations
We give a physicist's derivation of the geometrical (in the spirit of Duplantier–Sheffield) KPZ relations, via heat kernel methods. It gives a covariant way to define neighborhoods of fractals in 2D quantum gravity, and shows that these relations are in the realm of conformal field theory.
119148126
Scasimir Operator, Scentre and Representations of Uq(osp(1|2))
A bosonic operator of Uq(osp(1|2)) that anticommutes with the fermionic generators appears to be useful to describe the relations in the centre of Uq(osp(1|2)) for q a root of unity (in the unrestricted specialisation). As in the classical case, it also simplifies the classification of finite dimensional irreducible representations.
15486552
Comments on the links between SU(3) modular invariants, simple factors in the Jacobian of Fermat curves, and rational triangular billiards
We examine the proposal made recently that the su(3) modular invariant partition functions could be related to the geometry of the complex Fermat curves. Although a number of coincidences and similarities emerge between them and certain algebraic curves related to triangular billiards, their meaning remains obscure. In an attempt to go beyond the su(3) case, we show that any rational conformal field theory determines canonically a Riemann surface. Comment: 56 pages, 4 eps figures, LaTeX, uses epsf
5911478
Phase transition with the Berezinskii-Kosterlitz-Thouless singularity in the Ising model on a growing network.
We consider the ferromagnetic Ising model on a highly inhomogeneous network created by a growth process. We find that the phase transition in this system is characterized by the Berezinskii-Kosterlitz-Thouless singularity, although critical fluctuations are absent and the mean-field description is exact. Below this infinite order transition, the magnetization behaves as exp((-const/square root of(Tc-T)). We show that the critical point separates the phase with the power-law distribution of the linear response to a local field and the phase where this distribution rapidly decreases. We suggest that this phase transition occurs in a wide range of cooperative models with a strong infinite-range inhomogeneity.
173517385
A Short Introduction to Critical Interfaces in 2D
These notes are meant as a gentle introduction to the concepts of Loewner chains, local growth, Stochastic Loewner Evolutions (SLE) and their relationships to Conformal Field Theories (CFT). These concepts have played an important role in physics and mathematics during the recent years. The first section describes two discrete examples, the exploration process and loop-erased random walks. It can be read almost without any prerequisites. The aim is to show that even for curves defined purely in geometrical terms, it is useful to have a statistical mechanics viewpoint where the measure on curves is derived from a measure on local degrees of freedom of some model. A third model, diffusion-limited aggregation (DLA) is also introduced. The second section introduces Loewner chains and their relevance for the description of growth processes. A prerequisite is a minimal knowledge of complex analysis. The third section contains the derivation of the relevance of SLE in the description of interfaces when two properties, conformal invariance and the domain Markov property, are assumed/proved. The prerequisites are some knowledge of complex analysis and probability theory. The last section outlines the relation with Conformal Field Theory. This relation is via martingales and singular vectors. Again, the reader is assumed to have some basic knowledge of complex analysis and probability theory, and some familiarity with CFT. The discussion is informal. There is little or no claim at originality. We try to give some intuition based on explicit examples.
119287711
A dynamical time operator in Dirac's relativistic quantum mechanics
A self-adjoint dynamical time operator is introduced in Dirac's relativistic formulation of quantum mechanics and shown to satisfy a commutation relation with the Hamiltonian analogous to that of the position and momentum operators. The ensuing time-energy uncertainty relation involves the uncertainty in the instant of time when the wave packet passes a particular spatial position and the energy uncertainty associated with the wave packet at the same time, as envisaged originally by Bohr. The instantaneous rate of change of the position expectation value with respect to the simultaneous expectation value of the dynamical time operator is shown to be the phase velocity, in agreement with de Broglie's hypothesis of a particle associated wave whose phase velocity is larger than c. Thus, these two elements of the original basis and interpretation of quantum mechanics are integrated into its formal mathematical structure. Pauli's objection is shown to be resolved or circumvented. Possible relevance to current developments in electron channeling, in interference in time, in Zitterbewegung-like effects in spintronics, graphene and superconducting systems and in cosmology is noted.
38251987
Solution to the flavor problem of warped extra-dimension models.
A minimal solution to the flavor problem of warped extra-dimension models, i.e., the excessive mixed-chirality contribution to CP violation in K-K ¯ mixing arising from Kaluza-Klein (KK) gluon exchange, is proposed. Extending the strong-interaction gauge group in the bulk by an additional SU(3), and breaking this symmetry to QCD via boundary conditions, the constraints arising from the ε(K) parameter are significantly relaxed. As a result, KK scales M(KK)~2 TeV are consistent with all flavor observables without significant fine-tuning. The model predicts an extended Higgs sector featuring massive color-octet scalars and a tower of KK pseudoaxial gluon resonances, whose existence is not in conflict with recent LHC dijet bounds.
122582401
Monte Carlo evaluation of the muon-induced background in the GERDA double beta decay experiment
Abstract The new generation of experiments searching for neutrinoless double beta decay is aiming at a background level of 10 - 3 counts / ( kg keV y ) or better at the respective Q -values. Cosmic ray muons can be a significant contribution due to a number of physics processes. The GERmanium Detector Array, GERDA, located at the Gran Sasso underground laboratory in Italy, uses germanium enriched in 76 Ge as source and detector material. Germanium is submerged into liquid nitrogen or argon that acts as cooling medium and radiation shield simultaneously. A detailed G eant 4-based Monte Carlo simulation was performed to calculate the photon and neutron fluxes induced by cosmic ray muons. The prompt background contributions from γ -ray and neutron interactions as well as the delayed contributions due to the production of radioactive isotopes within the setup are given. The background can be reduced to the desired level with the muon veto system incorporated in the GERDA design.
13930079
The recurrent ultra-luminous X-ray transient NGC 253 ULX1
We present the results of ROSAT and XMM-Newton observations of the recurrent ultraluminous X-ray source (ULX) NGC 253 ULX I. This transient is one of the few ULXs that was detected during several outbursts. The luminosity reached 1.4 × 10 39 erg s -1 and 0.5 x 10 39 erg s -1 in the detections by ROSAT and XMM-Newton, respectively, indicating a black hole X-ray binary (BHXRB) with a mass of the compact object of ≥11 M ○. . In the ROSAT detection NGC 253 ULX1 showed significant variability, whereas the luminosity was constant in the detection from XMM-Newton. The XMM-Newton EPIC spectra are well-tit by a hremsstrahlung model (kT = 2.24 keV, N H = 1.74 x 10 20 cm -2 ), which can he used to describe a comptonized plasma. No counterpart was detected in the optical I, R, B, NUV and FUV bands to limits of 22.9, 24.2. 24.3, 22 and 23 mag, respectively, pointing at a XRB with a low mass companion.
133716710
New applications of silicon micromachining
The use of photolithography and anisotropic etching of silicon wafers to make strong, thin membranes has created a large family of miniature sensing devices such as pressure transducers and accelerometers. This report describes several entirely new devices in which silicon membranes are used for their strength and for their transparency to certain kinds of radiation. Two applications are described: a rugged alpha detector and a fluid sample cell for small-angle x-ray scattering. 8 refs., 12 figs., 2 tabs.