Symmetry conserving non-perturbative s-wave renormalization of the pion in hot and baryon dense medium

A non-perturbative s-wave renormalization of the pion in a hot and baryon rich medium is presented. This approach proceeds via a mapping of the canonical pion into the axial Noether's charge. The mapping was made dynamical in the Hartree-Fock-Bogoliubov random phase approximation (HFB-RPA). It is shown that this approach, while order mixing, is still symmetry conserving both in the baryon free and baryon rich sectors, at zero as well as finite temperature. The systematic character of this approach is emphasized and it is particularly argued that it may constitute an interesting alternative for the non-perturbative assessment of the nuclear matter saturation properties.Comment: Latex, 22 pages, 3 figure

Geometric-Phase-Effect Tunnel-Splitting Oscillations in Single-Molecule Magnets with Fourth-Order Anisotropy Induced by Orthorhombic Distortion

We analyze the interference between tunneling paths that occurs for a spin system with both fourth-order and second-order transverse anisotropy. Using an instanton approach, we find that as the strength of the second-order transverse anisotropy is increased, the tunnel splitting is modulated, with zeros occurring periodically. This effect results from the interference of four tunneling paths connecting easy-axis spin orientations and occurs in the absence of any magnetic field.Comment: 6 pages, 5 eps figures. Version published in EPL. Expanded from v1: Appendix added, references added, 1 figure added, others modified cosmeticall

Regularity of Ornstein-Uhlenbeck processes driven by a L{\'e}vy white noise

The paper is concerned with spatial and time regularity of solutions to linear stochastic evolution equation perturbed by L\'evy white noise "obtained by subordination of a Gaussian white noise". Sufficient conditions for spatial continuity are derived. It is also shown that solutions do not have in general \cadlag modifications. General results are applied to equations with fractional Laplacian. Applications to Burgers stochastic equations are considered as well.Comment: This is an updated version of the same paper. In fact, it has already been publishe

A new approach to bulk viscosity in strange quark matter at high densities

A new method is proposed to compute the bulk viscosity in strange quark matter at high densities. Using the method it is straightforward to prove that the bulk viscosity is positive definite, which is not so easy to accomplish in other approaches especially for multi-component fluids like strange quark matter with light up and down quarks and massive strange quarks.Comment: 7pages, talk given in SQM2008. Minor revisions, including clarification and updated reference

Tamari Lattices and the symmetric Thompson monoid

We investigate the connection between Tamari lattices and the Thompson group F, summarized in the fact that F is a group of fractions for a certain monoid F+sym whose Cayley graph includes all Tamari lattices. Under this correspondence, the Tamari lattice operations are the counterparts of the least common multiple and greatest common divisor operations in F+sym. As an application, we show that, for every n, there exists a length l chain in the nth Tamari lattice whose endpoints are at distance at most 12l/n.Comment: 35page

What is the Geometry of Superspace ?

We investigate certain properties of the Wheeler-DeWitt metric (for constant lapse) in canonical General Relativity associated with its non-definite nature. Contribution to the conference on Mach's principle: "From Newtons Bucket to Quantum Gravity", July 26-30 1993, Tuebingen, GermanyComment: 10 pages, Plain Te

Classifiers Based on Two-Layered Learning

Abstract. In this paper we present an exemplary classifier (classifica-tion algorithm) based on two-layered learning. In the first layer of learn-ing a collection of classifiers is induced from a part of original training data set. In the second layer classifiers are induced using patterns ex-tracted from already constructed classifiers on the basis of their perfor-mance on the remaining part of training data. We report results of exper-iments performed on the following data sets, well known from literature: diabetes, heart disease, australian credit (see [5]) and lymphography (see [4]). We compare the standard rough set method used to induce classi-fiers (see [1] for more details), based on minimal consistent decision rules (see [6]), with the classifier based on two-layered learning.

On the future of Gamma-Ray Burst Cosmology

With the understanding that the enigmatic Gamma-Ray Burts (GRBs) are beamed explosions, and with the recently discovered ``Ghirlanda-relation'', the dream of using GRBs as cosmological yardsticks may have come a few steps closer to reality. Assuming the Ghirlanda-relation is real, we have investigated possible constraints on cosmological parameters using a simulated future sample of a large number of GRBs inspired by the ongoing SWIFT mission. Comparing with constraints from a future sample of Type Ia supernovae, we find that GRBs are not efficient in constraining the amount of dark energy or its equation of state. The main reason for this is that very few bursts are available at low redshifts.Comment: 5 pages, 2 figures, matches version accepted for publication in JCA

Signaling, Entanglement, and Quantum Evolution Beyond Cauchy Horizons

Consider a bipartite entangled system half of which falls through the event horizon of an evaporating black hole, while the other half remains coherently accessible to experiments in the exterior region. Beyond complete evaporation, the evolution of the quantum state past the Cauchy horizon cannot remain unitary, raising the questions: How can this evolution be described as a quantum map, and how is causality preserved? What are the possible effects of such nonstandard quantum evolution maps on the behavior of the entangled laboratory partner? More generally, the laws of quantum evolution under extreme conditions in remote regions (not just in evaporating black-hole interiors, but possibly near other naked singularities and regions of extreme spacetime structure) remain untested by observation, and might conceivably be non-unitary or even nonlinear, raising the same questions about the evolution of entangled states. The answers to these questions are subtle, and are linked in unexpected ways to the fundamental laws of quantum mechanics. We show that terrestrial experiments can be designed to probe and constrain exactly how the laws of quantum evolution might be altered, either by black-hole evaporation, or by other extreme processes in remote regions possibly governed by unknown physics.Comment: Combined, revised, and expanded version of quant-ph/0312160 and hep-th/0402060; 13 pages, RevTeX, 2 eps figure