Phase Transitions in Granular Packings

We describe the contact network of granular packings by a frustrated lattice gas that contains steric frustration as essential ingredient. Two transitions are identified, a spin glass transition at the onset of Reynolds dilatancy and at lower densities a percolation transition. We describe the correlation functions that give rise to the singularities and propose some dynamical experiments

Critical Susceptibility Exponent Measured from Fe/W(110) Bilayers

The critical phase transition in ferromagnetic ultrathin Fe/W(110) films has been studied using the magnetic ac susceptibility. A statistically objective, unconstrained fitting of the susceptibility is used to extract values for the critical exponent (gamma), the critical temperature Tc, the critical amplitude (chi_o) and the range of temperature that exhibits power-law behaviour. A fitting algorithm was used to simultaneously minimize the statistical variance of a power law fit to individual experimental measurements of chi(T). This avoids systematic errors and generates objective fitting results. An ensemble of 25 measurements on many different films are analyzed. Those which permit an extended fitting range in reduced temperature lower than approximately .00475 give an average value gamma=1.76+-0.01. Bilayer films give a weighted average value of gamma = 1.75+-0.02. These results are in agreement with the -dimensional Ising exponent gamma= 7/4. Measurements that do not exhibit power-law scaling as close to Tc (especially films of thickness 1.75ML) show a value of gamma higher than the Ising value. Several possibilities are considered to account for this behaviour.Comment: -Submitted to Phys. Rev. B -Revtex4 Format -6 postscript figure

Statistical Mechanics of the Self-Gravitating Gas: I. Thermodynamic Limit and Phase Diagram

We provide a complete picture to the selfgravitating non-relativistic gas at thermal equilibrium using Monte Carlo simulations, analytic mean field methods (MF) and low density expansions. The system is shown to possess an infinite volume limit in the grand canonical (GCE), canonical (CE) and microcanonical (MCE) ensembles when(N, V) --> infinity, keeping N/ V^{1/3} fixed. We compute the equation of state (we do not assume it as is customary), as well as the energy, free energy, entropy, chemical potential, specific heats, compressibi- lities and speed of sound;we analyze their properties, signs and singularities. All physical quantities turn out to depend on a single variable eta = G m^2 N/ [V^{1/3} T] that is kept fixed in the N--> infinity and V --> infinity limit. The system is in a gaseous phase for eta < eta_T and collapses into a dense objet for eta > \eta_T in the CE with the pressure becoming large and negative. At eta simeq eta_T the isothermal compressibility diverges. Our Monte Carlo simulations yield eta_T simeq 1.515. PV/[NT] = f(eta) and all physical magni- tudes exhibit a square root branch point at eta = eta_C > eta_T. The MF for spherical symmetry yields eta_C = 1.561764.. while Monte Carlo on a cube yields eta_C simeq 1.540.The function f(eta) has a second Riemann sheet which is only physically realized in the MCE.In the MCE, the collapse phase transition takes place in this second sheet near eta_MC = 1.26 and the pressure and temperature are larger in the collapsed phase than in the gas phase.Both collapse phase transitions (CE and MCE) are of zeroth order since the Gibbs free energy jumps at the transitions. f(eta), obeys in MF a first order non-linear differential equation of first kind Abel's type.The MF gives an extremely accurate picture in agreement with Monte Carlo both in the CE and MCE.Comment: Latex, 51 pages, 15 .ps figures, to appear in Nucl. Phys.

Short-time dynamics and magnetic critical behavior of two-dimensional random-bond Potts model

The critical behavior in the short-time dynamics for the random-bond Potts ferromagnet in two-dimensions is investigated by short-time dynamic Monte Carlo simulations. The numerical calculations show that this dynamic approach can be applied efficiently to study the scaling characteristic, which is used to estimate the critical exponents theta, beta/nu and z for the quenched disorered systems from the power-law behavior of the kth moments of magnetizations.Comment: 10 pages, 4 figures Soft Condensed Matte

The Quark-Hadron Phase Transition, QCD Lattice Calculations and Inhomogeneous Big-Bang Nucleosynthesis

We review recent lattice QCD results for the surface tension at the finite temperature quark-hadron phase transition and discuss their implications on the possible scale of inhomogeneities. In the quenched approximation the average distance between nucleating centers is smaller than the diffusion length of a protron, so that inhomogeneities are washed out by the time nucleosynthesis sets in. Consequently the baryon density fluctuations formed by a QCD phase transition in the early universe cannot significantly affect standard big-bang nucleosynthesis calculations and certainly cannot allow baryons to close the universe. At present lattice results are inconclusive when dynamical fermions are included.Comment: 8 pages, LaTe

Collective motions in globally coupled tent maps with stochastic updating

We study a generalization of globally coupled maps, where the elements are updated with probability $p$. When $p$ is below a threshold $p_c$, the collective motion vanishes and the system is the stationary state in the large size limit. We present the linear stability analysis.Comment: 6 pages including 5 figure

Polariton propagation in weak confinement quantum wells

Exciton-polariton propagation in a quantum well, under centre-of-mass quantization, is computed by a variational self-consistent microscopic theory. The Wannier exciton envelope functions basis set is given by the simple analytical model of ref. [1], based on pure states of the centre-of-mass wave vector, free from fitting parameters and "ad hoc" (the so called additional boundary conditions-ABCs) assumptions. In the present paper, the former analytical model is implemented in order to reproduce the centre-of-mass quantization in a large range of quantum well thicknesses (5a_B < L < inf.). The role of the dynamical transition layer at the well/barrier interfaces is discussed at variance of the classical Pekar's dead-layer and ABCs. The Wannier exciton eigenstates are computed, and compared with various theoretical models with different degrees of accuracy. Exciton-polariton transmission spectra in large quantum wells (L>> a_B) are computed and compared with experimental results of Schneider et al.\cite{Schneider} in high quality GaAs samples. The sound agreement between theory and experiment allows to unambiguously assign the exciton-polariton dips of the transmission spectrum to the pure states of the Wannier exciton center-of-mass quantization.Comment: 15 pages, 15 figures; will appear in Phys.Rev.

Tunneling of quantum rotobreathers

We analyze the quantum properties of a system consisting of two nonlinearly coupled pendula. This non-integrable system exhibits two different symmetries: a permutational symmetry (permutation of the pendula) and another one related to the reversal of the total momentum of the system. Each of these symmetries is responsible for the existence of two kinds of quasi-degenerated states. At sufficiently high energy, pairs of symmetry-related states glue together to form quadruplets. We show that, starting from the anti-continuous limit, particular quadruplets allow us to construct quantum states whose properties are very similar to those of classical rotobreathers. By diagonalizing numerically the quantum Hamiltonian, we investigate their properties and show that such states are able to store the main part of the total energy on one of the pendula. Contrary to the classical situation, the coupling between pendula necessarily introduces a periodic exchange of energy between them with a frequency which is proportional to the energy splitting between quasi-degenerated states related to the permutation symmetry. This splitting may remain very small as the coupling strength increases and is a decreasing function of the pair energy. The energy may be therefore stored in one pendulum during a time period very long as compared to the inverse of the internal rotobreather frequency.Comment: 20 pages, 11 figures, REVTeX4 styl