Gauss Sums and Quantum Mechanics

By adapting Feynman's sum over paths method to a quantum mechanical system whose phase space is a torus, a new proof of the Landsberg-Schaar identity for quadratic Gauss sums is given. In contrast to existing non-elementary proofs, which use infinite sums and a limiting process or contour integration, only finite sums are involved. The toroidal nature of the classical phase space leads to discrete position and momentum, and hence discrete time. The corresponding `path integrals' are finite sums whose normalisations are derived and which are shown to intertwine cyclicity and discreteness to give a finite version of Kelvin's method of images.Comment: 14 pages, LaTe

Flow at the SPS and RHIC as a Quark Gluon Plasma Signature

Radial and elliptic flow in non-central heavy ion collisions can constrain the effective Equation of State(EoS) of the excited nuclear matter. To this end, a model combining relativistic hydrodynamics and a hadronic transport code(RQMD [17]) is developed. For an EoS with a first order phase transition, the model reproduces both the radial and elliptic flow data at the SPS. With the EoS fixed from SPS data, we quantify predictions at RHIC where the Quark Gluon Plasma(QGP) pressure is expected to drive additional radial and elliptic flow. Currently, the strong elliptic flow observed in the first RHIC measurements does not conclusively signal this nascent QGP pressure. Additional measurements are suggested to pin down the EoS.Comment: 4 pages, 4 figures. Revised. Included discussed of v_2 (p_t) vs. b and comparison to STAR dat

Density of states in random lattices with translational invariance

We propose a random matrix approach to describe vibrational excitations in disordered systems. The dynamical matrix M is taken in the form M=AA^T where A is some real (not generally symmetric) random matrix. It guaranties that M is a positive definite matrix which is necessary for mechanical stability of the system. We built matrix A on a simple cubic lattice with translational invariance and interaction between nearest neighbors. We found that for certain type of disorder phonons cannot propagate through the lattice and the density of states g(w) is a constant at small w. The reason is a breakdown of affine assumptions and inapplicability of the elasticity theory. Young modulus goes to zero in the thermodynamic limit. It strongly reminds of the properties of a granular matter at the jamming transition point. Most of the vibrations are delocalized and similar to diffusons introduced by Allen, Feldman et al., Phil. Mag. B v.79, 1715 (1999).Comment: 4 pages, 5 figure

Evidence of early multi-strange hadron freeze-out in high energy nuclear collisions

Recently reported transverse momentum distributions of strange hadrons produced in Pb(158AGeV) on Pb collisions and corresponding results from the relativistic quantum molecular dynamics (RQMD) approach are examined. We argue that the experimental observations favor a scenario in which multi-strange hadrons are formed and decouple from the system rather early at large energy densities (around 1 GeV/fm$^3$). The systematics of the strange and non-strange particle spectra indicate that the observed transverse flow develops mainly in the late hadronic stages of these reactions.Comment: 4 pages, 4 figure

Dynamics of localized structures in vector waves

Dynamical properties of topological defects in a twodimensional complex vector field are considered. These objects naturally arise in the study of polarized transverse light waves. Dynamics is modeled by a Vector Complex Ginzburg-Landau Equation with parameter values appropriate for linearly polarized laser emission. Creation and annihilation processes, and selforganization of defects in lattice structures, are described. We find "glassy" configurations dominated by vectorial defects and a melting process associated to topological-charge unbinding.Comment: 4 pages, 5 figures included in the text. To appear in Phys. Rev. Lett. (2000). Related material at http://www.imedea.uib.es/Nonlinear and http://www.imedea.uib.es/Photonics . In this new version, Fig. 3 has been replaced by a better on

Thermal analysis of hadron multiplicities from relativistic quantum molecular dynamics

Some questions arising in the application of the thermal model to hadron production in heavy ion collisions are studied. We do so by applying the thermal model of hadron production to particle yields calculated by the microscopic transport model RQMD(v2.3). We study the bias of incomplete information about the final hadronic state on the extraction of thermal parameters.It is found that the subset of particles measured typically in the experiments looks more thermal than the complete set of stable particles. The hadrons which show the largest deviations from thermal behaviour in RQMD(v2.3) are the multistrange baryons and antibaryons. We also looked at the influence of rapidity cuts on the extraction of thermal parameters and found that they lead to different thermal parameters and larger disagreement between the RQMD yields and the thermal model.Comment: 12 pages, 2 figures, uses REVTEX, only misprint and stylistic corrections, to appear in Physical Review

Sparse random matrices and vibrational spectra of amorphous solids

A random matrix approach is used to analyze the vibrational properties of amorphous solids. We investigated a dynamical matrix M=AA^T with non-negative eigenvalues. The matrix A is an arbitrary real NxN sparse random matrix with n independent non-zero elements in each row. The average values =0 and dispersion =V^2 for all non-zero elements. The density of vibrational states g(w) of the matrix M for N,n >> 1 is given by the Wigner quarter circle law with radius independent of N. We argue that for n^2 << N this model can be used to describe the interaction of atoms in amorphous solids. The level statistics of matrix M is well described by the Wigner surmise and corresponds to repulsion of eigenfrequencies. The participation ratio for the major part of vibrational modes in three dimensional system is about 0.2 - 0.3 and independent of N. Together with term repulsion it indicates clearly to the delocalization of vibrational excitations. We show that these vibrations spread in space by means of diffusion. In this respect they are similar to diffusons introduced by Allen, Feldman, et al., Phil. Mag. B 79, 1715 (1999) in amorphous silicon. Our results are in a qualitative and sometimes in a quantitative agreement with molecular dynamic simulations of real and model glasses.Comment: 24 pages, 7 figure

Annular electroconvection with shear

We report experiments on convection driven by a radial electrical force in suspended annular smectic A liquid crystal films. In the absence of an externally imposed azimuthal shear, a stationary one-dimensional (1D) pattern consisting of symmetric vortex pairs is formed via a supercritical transition at the onset of convection. Shearing reduces the symmetries of the base state and produces a traveling 1D pattern whose basic periodic unit is a pair of asymmetric vortices. For a sufficiently large shear, the primary bifurcation changes from supercritical to subcritical. We describe measurements of the resulting hysteresis as a function of the shear at radius ratio $\eta \sim 0.8$. This simple pattern forming system has an unusual combination of symmetries and control parameters and should be amenable to quantitative theoretical analysis.Comment: 12 preprint pages, 3 figures in 2 parts each. For more info, see http://mobydick.physics.utoronto.c

Examine the species and beam-energy dependence of particle spectra using Tsallis Statistics

Tsallis Statistics was used to investigate the non-Boltzmann distribution of particle spectra and their dependence on particle species and beam energy in the relativistic heavy-ion collisions at SPS and RHIC. Produced particles are assumed to acquire radial flow and be of non-extensive statistics at freeze-out. J/psi and the particles containing strangeness were examined separately to study their radial flow and freeze-out. We found that the strange hadrons approach equilibrium quickly from peripheral to central A+A collisions and they tend to decouple earlier from the system than the light hadrons but with the same final radial flow. These results provide an alternative picture of freeze-outs: a thermalized system is produced at partonic phase; the hadronic scattering at later stage is not enough to maintain the system in equilibrium and does not increase the radial flow of the copiously produced light hadrons. The J/psi in Pb+Pb collisions at SPS is consistent with early decoupling and obtains little radial flow. The J/psi spectra at RHIC are also inconsistent with the bulk flow profile.Comment: 12 pages, 4 figures, added several references and some clarifications et

Phase chaos in the anisotropic complex Ginzburg-Landau Equation

Of the various interesting solutions found in the two-dimensional complex Ginzburg-Landau equation for anisotropic systems, the phase-chaotic states show particularly novel features. They exist in a broader parameter range than in the isotropic case, and often even broader than in one dimension. They typically represent the global attractor of the system. There exist two variants of phase chaos: a quasi-one dimensional and a two-dimensional solution. The transition to defect chaos is of intermittent type.Comment: 4 pages RevTeX, 5 figures, little changes in figures and references, typos removed, accepted as Rapid Commun. in Phys. Rev.