Negative Temperature States in the Discrete Nonlinear Schroedinger Equation

We explore the statistical behavior of the discrete nonlinear Schroedinger equation. We find a parameter region where the system evolves towards a state characterized by a finite density of breathers and a negative temperature. Such a state is metastable but the convergence to equilibrium occurs on astronomical time scales and becomes increasingly slower as a result of a coarsening processes. Stationary negative-temperature states can be experimentally generated via boundary dissipation or from free expansions of wave packets initially at positive temperature equilibrium.Comment: 4 pages, 5 figure

Cathodoluminescence Study of Defects in III-V Substrates and Structures

Solid state detector cathodoluminescence studies of semiconducting and semi-insulating GaAs and InP crystals, were performed. The origin of the dislocation contrast in GaAs:Si doped substrates, in the carrier concentration range from 1016 to 6 · 1018 cm-3, were discussed. The image contrast was explained on the basis of the emission efficiency versus carrier concentration curve, obtained in the transmission mode. Single dislocations and dislocation arrangements in addition to growth striations, clusters and precipitate-like microdefects were evidenced. The above mentioned microdefects were detected in GaAs: Te, S and Si doped and InP: Sn doped specimens. Commercial InP:Sn and S doped crystals by different manufacturers were also tested in order to perform a comprehensive evaluation of the defect content. Finally, combining emission and transmission cathodoluminescence, Si and Ge detectors at different beam energies, the defect distribution of different layers in simple and double heterostructures was determined in a non-destructive way. MBE InGaAs/InP and LPE InGaAsP/InP structures, employed as semiconductor detectors and lasers, were investigated

Ground-state Properties of Small-Size Nonlinear Dynamical Lattices

We investigate the ground state of a system of interacting particles in small nonlinear lattices with M > 2 sites, using as a prototypical example the discrete nonlinear Schroedinger equation that has been recently used extensively in the contexts of nonlinear optics of waveguide arrays, and Bose-Einstein condensates in optical lattices. We find that, in the presence of attractive interactions, the dynamical scenario relevant to the ground state and the lowest-energy modes of such few-site nonlinear lattices reveals a variety of nontrivial features that are absent in the large/infinite lattice limits: the single-pulse solution and the uniform solution are found to coexist in a finite range of the lattice intersite coupling where, depending on the latter, one of them represents the ground state; in addition, the single-pulse mode does not even exist beyond a critical parametric threshold. Finally, the onset of the ground state (modulational) instability appears to be intimately connected with a non-standard (``double transcritical'') type of bifurcation that, to the best of our knowledge, has not been reported previously in other physical systems.Comment: 7 pages, 4 figures; submitted to PR

Phase transitions as topology changes in configuration space: an exact result

The phase transition in the mean-field XY model is shown analytically to be related to a topological change in its configuration space. Such a topology change is completely described by means of Morse theory allowing a computation of the Euler characteristic--of suitable submanifolds of configuration space--which shows a sharp discontinuity at the phase transition point, also at finite N. The present analytic result provides, with previous work, a new key to a possible connection of topological changes in configuration space as the origin of phase transitions in a variety of systems.Comment: REVTeX file, 5 pages, 1 PostScript figur

Spectral Properties of Coupled Bose-Einstein Condensates

We investigate the energy spectrum structure of a system of two (identical) interacting bosonic wells occupied by N bosons within the Schwinger realization of the angular momentum. This picture enables us to recognize the symmetry properties of the system Hamiltonian H and to use them for characterizing the energy eigenstates. Also, it allows for the derivation of the single-boson picture which is shown to be the background picture naturally involved by the secular equation for H. After deriving the corresponding eigenvalue equation, we recast it in a recursive N-dependent form which suggests a way to generate the level doublets (characterizing the H spectrum) via suitable inner parameters. Finally, we show how the presence of doublets in the spectrum allows to recover, in the classical limit, the symmetry breaking effect that characterizes the system classically.Comment: 8 pages, 3 figures; submitted to Phys. Rev. A. The present extended form replaces the first version in the letter forma

The Origins of Phase Transitions in Small Systems

The identification and classification of phases in small systems, e.g. nuclei, social and financial networks, clusters, and biological systems, where the traditional definitions of phase transitions are not applicable, is important to obtain a deeper understanding of the phenomena observed in such systems. Within a simple statistical model we investigate the validity and applicability of different classification schemes for phase transtions in small systems. We show that the whole complex temperature plane contains necessary information in order to give a distinct classification.Comment: 3 pages, 4 figures, revtex 4 beta 5, for further information see http://www.smallsystems.d

Geometry and observables in (2+1)-gravity

We review the geometrical properties of vacuum spacetimes in (2+1)-gravity with vanishing cosmological constant. We explain how these spacetimes are characterised as quotients of their universal cover by holonomies. We explain how this description can be used to clarify the geometrical interpretation of the fundamental physical variables of the theory, holonomies and Wilson loops. In particular, we discuss the role of Wilson loop observables as the generators of the two fundamental transformations that change the geometry of (2+1)-spacetimes, grafting and earthquake. We explain how these variables can be determined from realistic measurements by an observer in the spacetime.Comment: Talk given at 2nd School and Workshop on Quantum Gravity and Quantum Geometry (Corfu, September 13-20 2009); 10 pages, 13 eps figure

Weak and strong chaos in Fermi-Pasta-Ulam models and beyond

We briefly review some of the most relevant results that our group obtained in the past, while investigating the dynamics of the Fermi-Pasta-Ulam (FPU) models. The first result is the numerical evidence of the existence of two different kinds of transitions in the dynamics of the FPU models: (i) A stochasticity threshold (ST), characterized by a value of the energy per degree of freedom below which the overwhelming majority of the phase space trajectories are regular (vanishing Lyapunov exponents). It tends to vanish as the number N of degrees of freedom is increased. (ii) A strong stochasticity threshold (SST), characterized by a value of the energy per degree of freedom at which a crossover appears between two different power laws of the energy dependence of the largest Lyapunov exponent, which phenomenologically corresponds to the transition between weak and strong chaotic regimes. It is stable with N. The second result is the development of a Riemannian geometric theory to explain the origin of Hamiltonian chaos. Starting this theory has been motivated by the inadequacy of the approach based on homoclinic intersections to explain the origin of chaos in systems of arbitrarily large N, or arbitrarily far from quasi-integrability, or displaying a transition between weak and strong chaos. Finally, the third result stems from the search for the transition between weak and strong chaos in systems other than FPU. Actually, we found that a very sharp SST appears as the dynamical counterpart of a thermodynamic phase transition, which in turn has led, in the light of the Riemannian theory of chaos, to the development of a topological theory of phase transitions. (C) 2005 American Institute of Physics

The Torus Universe in the Polygon Approach to 2+1-Dimensional Gravity

In this paper we describe the matter-free toroidal spacetime in 't Hooft's polygon approach to 2+1-dimensional gravity (i.e. we consider the case without any particles present). Contrary to earlier results in the literature we find that it is not possible to describe the torus by just one polygon but we need at least two polygons. We also show that the constraint algebra of the polygons closes.Comment: 18 pages Latex, 13 eps-figure