Wavelet representations and Fock space on positive matrices

We show that every biorthogonal wavelet determines a representation by operators on Hilbert space satisfying simple identities, which captures the established relationship between orthogonal wavelets and Cuntz-algebra representations in that special case. Each of these representations is shown to have tractable finite-dimensional co-invariant doubly-cyclic subspaces. Further, motivated by these representations, we introduce a general Fock-space Hilbert space construction which yields creation operators containing the Cuntz--Toeplitz isometries as a special case.Comment: 32 pages, LaTeX ("amsart" document class), one EPS graphic file used for shading, accepted March 2002 for J. Funct. Ana

Indications for a Detonating Quark-Gluon Plasma

We propose a mechanism which naturally contains the relation $\mu_{B} = 3\mu_{S}$ of the hadronic gas produced in heavy-ion collisions at CERN. Our starting assumption is the existence of a sharp front separating the quark-gluon plasma phase from the hadronic phase. Energy-momentum conservation across the front leads to the following consequences for an adiabatic process a) The baryon chemical potential, $\mu_{B}$, is approximately continuous across the front. b) The temperature in the hadronic gas is higher than the phase transition temperature due to superheating. c) In the region covered by the experiments the velocity of the hadronic gas approximately equals the speed of sound in the hadronic gas.Comment: Latex file 9 pages + 6 figures available as postscript file

Measurements of critical current diffraction patterns in annular Josephson junctions

We report systematic measurements of the critical current versus magnetic field patterns of annular Josephson junctions in a wide magnetic field range. A modulation of the envelope of the pattern, which depends on the junction width, is observed. The data are compared with theory and good agreement is found.Comment: 4 pages, 5 figure

Transition from a quark-gluon plasma in the presence of a sharp front

The effect of a sharp front separating the quark-gluon plasma phase from the hadronic phase is investigated. Energy-momentum conservation and baryon number conservation constrain the possible temperature jump across the front. If one assumes that the temperature in the hadronic phase is $T\simeq$ 200 MeV , as has been suggested by numerous results from relativistic ion collisions, one can determine the corresponding temperature in the quark phase with the help of continuity equations across the front. The calculations reveal that the quark phase must be in a strongly supercooled state. The stability of this solution with respect to minor modifications is investigated. In particular the effect of an admixture of hadronic matter in the quark phase (e.g. in the form of bubbles) is considered in detail. In the absence of admixture the transition proceeds via a detonation transition and is accompanied by a substantial super-cooling of the quark-gluon plasma phase. The detonation is accompanied by less supercooling if a small fraction of bubbles is allowed. By increasing the fraction of bubbles the supercooling becomes weaker and eventually the transition proceeds via a smoother deflagration wave.Comment: 10 pages, manuscript in TeX, 9 figures available as Postscript files, CERN-TH 6923/9

The glassy response of solid He-4 to torsional oscillations

We calculated the glassy response of solid He-4 to torsional oscillations assuming a phenomenological glass model. Making only a few assumptions about the distribution of glassy relaxation times in a small subsystem of otherwise rigid solid He-4, we can account for the magnitude of the observed period shift and concomitant dissipation peak in several torsion oscillator experiments. The implications of the glass model for solid He-4 are threefold: (1) The dynamics of solid He-4 is governed by glassy relaxation processes. (2) The distribution of relaxation times varies significantly between different torsion oscillator experiments. (3) The mechanical response of a torsion oscillator does not require a supersolid component to account for the observed anomaly at low temperatures, though we cannot rule out its existence.Comment: 9 pages, 4 figures, presented at QFS200

Dielectric spectra analysis: reliable parameter estimation using interval analysis

Dielectric spectroscopy is an extremely versatile method for characterizing the molecular dynamics over a large range of time scales. Unfortunately, the extraction of model parameters by data fitting is still a crucial problem which is now solved by our program S.A.D.E. S.A.D.E. is based on the algorithm S.I.V.I.A. which was proposed and implemented by Jaulin in order to solve constraint satisfaction problems. The problem of dielectric data analysis is reduced to a problem of choosing the appropriate physical model. In this article, Debye relaxations were used and validated to fit the relaxations of a DGEBA prepolymer and the polarization of the spectrometer electrodes. The conductivity was evaluated too

Wavelets and graph C∗C^*-algebras

Here we give an overview on the connection between wavelet theory and representation theory for graph $C^{\ast}$-algebras, including the higher-rank graph $C^*$-algebras of A. Kumjian and D. Pask. Many authors have studied different aspects of this connection over the last 20 years, and we begin this paper with a survey of the known results. We then discuss several new ways to generalize these results and obtain wavelets associated to representations of higher-rank graphs. In \cite{FGKP}, we introduced the "cubical wavelets" associated to a higher-rank graph. Here, we generalize this construction to build wavelets of arbitrary shapes. We also present a different but related construction of wavelets associated to a higher-rank graph, which we anticipate will have applications to traffic analysis on networks. Finally, we generalize the spectral graph wavelets of \cite{hammond} to higher-rank graphs, giving a third family of wavelets associated to higher-rank graphs

Supersymmetry without R-parity : Constraints from Leptonic Phenomenology

R-parity conservation is an {\it ad hoc} assumption in the most popular version of the supersymmetric standard model. Most studies of models which do allow for R-parity violation have been restricted to various limiting scenarios. The single-VEV parametrization used in this paper provides a workable framework to analyze phenomenology of the most general theory of SUSY without R-parity. We perform a comprehensive study of leptonic phenomenology at tree-level. Experimental constraints on various processes are studied individually and then combined to yield regions of admissible parameter space. In particular, we show that large R-parity violating bilinear couplings are not ruled out, especially for large $\tan\beta$.Comment: 56 pages Revtex with figures incorporated; typos (including transcription typo in Table II) and minor corrections; proof-read version, to appear in Phys. Rev.

Dielectric and conductivity relaxation in mixtures of glycerol with LiCl

We report a thorough dielectric characterization of the alpha relaxation of glass forming glycerol with varying additions of LiCl. Nine salt concentrations from 0.1 - 20 mol% are investigated in a frequency range of 20 Hz - 3 GHz and analyzed in the dielectric loss and modulus representation. Information on the dc conductivity, the dielectric relaxation time (from the loss) and the conductivity relaxation time (from the modulus) is provided. Overall, with increasing ion concentration, a transition from reorientationally to translationally dominated behavior is observed and the translational ion dynamics and the dipolar reorientational dynamics become successively coupled. This gives rise to the prospect that by adding ions to dipolar glass formers, dielectric spectroscopy may directly couple to the translational degrees of freedom determining the glass transition, even in frequency regimes where usually strong decoupling is observed.Comment: 8 pages, 7 figure

Defects and glassy dynamics in solid He-4: Perspectives and current status

We review the anomalous behavior of solid He-4 at low temperatures with particular attention to the role of structural defects present in solid. The discussion centers around the possible role of two level systems and structural glassy components for inducing the observed anomalies. We propose that the origin of glassy behavior is due to the dynamics of defects like dislocations formed in He-4. Within the developed framework of glassy components in a solid, we give a summary of the results and predictions for the effects that cover the mechanical, thermodynamic, viscoelastic, and electro-elastic contributions of the glassy response of solid He-4. Our proposed glass model for solid He-4 has several implications: (1) The anomalous properties of He-4 can be accounted for by allowing defects to freeze out at lowest temperatures. The dynamics of solid He-4 is governed by glasslike (glassy) relaxation processes and the distribution of relaxation times varies significantly between different torsional oscillator, shear modulus, and dielectric function experiments. (2) Any defect freeze-out will be accompanied by thermodynamic signatures consistent with entropy contributions from defects. It follows that such entropy contribution is much smaller than the required superfluid fraction, yet it is sufficient to account for excess entropy at lowest temperatures. (3) We predict a Cole-Cole type relation between the real and imaginary part of the response functions for rotational and planar shear that is occurring due to the dynamics of defects. Similar results apply for other response functions. (4) Using the framework of glassy dynamics, we predict low-frequency yet to be measured electro-elastic features in defect rich He-4 crystals. These predictions allow one to directly test the ideas and very presence of glassy contributions in He-4.Comment: 33 pages, 13 figure