Microscopic spectral density in random matrix models for chiral and diquark condensation

We examine random matrix models of QCD which are capable of supporting both chiral and diquark condensation. A numerical study of the spectral densities near zero virtuality shows that the introduction of color in the interactions does not alter the one-body results imposed by chiral symmetry. A model with three colors has the spectral density predicted for the chiral ensemble with a Dyson index beta = 2; a pseudoreal model with two colors exhibits the spectral density of the chiral ensemble with beta = 1.Comment: 6 pages, 3 eps figures, uses revtex4 and graphicx. v2 : minor editions, Fig. 3 shows relative deviations rather than absolute. Version to appear in PR

Random matrix model for antiferromagnetism and superconductivity on a two-dimensional lattice

We suggest a new mean field method for studying the thermodynamic competition between magnetic and superconducting phases in a two-dimensional square lattice. A partition function is constructed by writing microscopic interactions that describe the exchange of density and spin-fluctuations. A block structure dictated by spin, time-reversal, and bipartite symmetries is imposed on the single-particle Hamiltonian. The detailed dynamics of the interactions are neglected and replaced by a normal distribution of random matrix elements. The resulting partition function can be calculated exactly. The thermodynamic potential has a structure which depends only on the spectrum of quasiparticles propagating in fixed condensation fields, with coupling constants that can be related directly to the variances of the microscopic processes. The resulting phase diagram reveals a fixed number of phase topologies whose realizations depend on a single coupling-parameter ratio, alpha. Most phase topologies are realized for a broad range of values of alpha and can thus be considered robust with respect to moderate variations in the detailed description of the underlying interactions.Comment: 21 pages, 8 figures, RevTex 4. Minor grammatical errors corrected in the last versio

Random matrix models for chiral and diquark condensation

We consider random matrix models for the thermodynamic competition between chiral symmetry breaking and diquark condensation in QCD at finite temperature and finite baryon density. The models produce mean field phase diagrams whose topology depends solely on the global symmetries of the theory. We discuss the block structure of the interactions that is imposed by chiral, spin, and color degrees of freedom and comment on the treatment of density and temperature effects. Extension of the coupling parameters to a larger class of theories allows us to investigate the robustness of the phase topology with respect to variations in the dynamics of the interactions. We briefly study the phase structure as a function of coupling parameters and the number of colors.Comment: 6 pages, 2 figures, proceedings of the workshop "Three Days of Hadronic Physics", Joint Meeting Heidelberg-Liege-Paris-Rostock, 16/12/2004-18/12/2004, Sol Cress, Spa, Belgium. v2: typographical errors corrected in reference

Single nanoparticle measurement techniques

Various single particle measuring techniques are briefly reviewed and the basic concepts of a new micro-SQUID technique are discussed. It allows measurements of the magnetization reversal of single nanometer-sized particles at low temperature. The influence of the measuring technique on the system of interest is discussed.Comment: 3 pages, 3 figures, conference proceedings of MMM 1999, San Jose, 15-18 Nov., session number BE-0

Formulas for Continued Fractions. An Automated Guess and Prove Approach

We describe a simple method that produces automatically closed forms for the coefficients of continued fractions expansions of a large number of special functions. The function is specified by a non-linear differential equation and initial conditions. This is used to generate the first few coefficients and from there a conjectured formula. This formula is then proved automatically thanks to a linear recurrence satisfied by some remainder terms. Extensive experiments show that this simple approach and its straightforward generalization to difference and $q$-difference equations capture a large part of the formulas in the literature on continued fractions.Comment: Maple worksheet attache

Infinite Kinematic Self-Similarity and Perfect Fluid Spacetimes

Perfect fluid spacetimes admitting a kinematic self-similarity of infinite type are investigated. In the case of plane, spherically or hyperbolically symmetric space-times the field equations reduce to a system of autonomous ordinary differential equations. The qualitative properties of solutions of this system of equations, and in particular their asymptotic behavior, are studied. Special cases, including some of the invariant sets and the geodesic case, are examined in detail and the exact solutions are provided. The class of solutions exhibiting physical self-similarity are found to play an important role in describing the asymptotic behavior of the infinite kinematic self-similar models.Comment: 38 pages, 6 figures. Accepted for publication in General Relativity & Gravitatio

Direct observation of the quantum critical point in heavy fermion CeRhSi3_3

We report on muon spin rotation studies of the noncentrosymmetric heavy fermion antiferromagnet CeRhSi$_3$. A drastic and monotonic suppression of the internal fields, at the lowest measured temperature, was observed upon an increase of external pressure. Our data suggest that the ordered moments are gradually quenched with increasing pressure, in a manner different from the pressure dependence of the N\'eel temperature. At \unit{23.6}{kbar}, the ordered magnetic moments are fully suppressed via a second-order phase transition, and $T_{\rm{N}}$ is zero. Thus, we directly observed the quantum critical point at \unit{23.6}{kbar} hidden inside the superconducting phase of CeRhSi$_3$

Universal Fluctuation of the Hall Conductance in the Random Magnetic Field

We show that the RMS fluctuation of the antisymmetric part of the Hall conductance of a planar mesoscopic metal in a random magnetic field with zero average is universal, of the order of $e^2/h$, independent of the amplitude of the random magnetic field and the diffusion coefficient even in the weak field limit. This quantity is exactly zero in the case of ordinary scalar disorder. We propose an experiment to measure this surprising effect, and also discuss its implications on the localization physics of this system. Our result applies to some other systems with broken time-reversal ({\bf T}) symmetry.Comment: 4 pages, Revtex 3.0; added the paragraph regarding applicability to other systems with broken T-invariance, misc. minor change

Kondo engineering : from single Kondo impurity to the Kondo lattice

In the first step, experiments on a single cerium or ytterbium Kondo impurity reveal the importance of the Kondo temperature by comparison to other type of couplings like the hyperfine interaction, the crystal field and the intersite coupling. The extension to a lattice is discussed. Emphasis is given on the fact that the occupation number $n_f$ of the trivalent configuration may be the implicit key variable even for the Kondo lattice. Three $(P, H, T)$ phase diagrams are discussed: CeRu$_2$Si$_2$, CeRhIn$_5$ and SmS