Ensemble Inequivalence in Mean-field Models of Magnetism

Mean-field models, while they can be cast into an {\it extensive} thermodynamic formalism, are inherently {\it non additive}. This is the basic feature which leads to {\it ensemble inequivalence} in these models. In this paper we study the global phase diagram of the infinite range Blume-Emery-Griffiths model both in the {\it canonical} and in the {\it microcanonical} ensembles. The microcanonical solution is obtained both by direct state counting and by the application of large deviation theory. The canonical phase diagram has first order and continuous transition lines separated by a tricritical point. We find that below the tricritical point, when the canonical transition is first order, the phase diagrams of the two ensembles disagree. In this region the microcanonical ensemble exhibits energy ranges with negative specific heat and temperature jumps at transition energies. These two features are discussed in a general context and the appropriate Maxwell constructions are introduced. Some preliminary extensions of these results to weakly decaying nonintegrable interactions are presented.Comment: Chapter of the forthcoming "Lecture Notes in Physics" volume: ``Dynamics and Thermodynamics of Systems with Long Range Interactions'', T. Dauxois, S. Ruffo, E. Arimondo, M. Wilkens Eds., Lecture Notes in Physics Vol. 602, Springer (2002). (see http://link.springer.de/series/lnpp/

Thermodynamics and collapse of self-gravitating Brownian particles in D dimensions

We address the thermodynamics (equilibrium density profiles, phase diagram, instability analysis...) and the collapse of a self-gravitating gas of Brownian particles in D dimensions, in both canonical and microcanonical ensembles. In the canonical ensemble, we derive the analytic form of the density scaling profile which decays as f(x)=x^{-\alpha}, with alpha=2. In the microcanonical ensemble, we show that f decays as f(x)=x^{-\alpha_{max}}, where \alpha_{max} is a non-trivial exponent. We derive exact expansions for alpha_{max} and f in the limit of large D. Finally, we solve the problem in D=2, which displays rather rich and peculiar features

Thermodynamics with long-range interactions: from Ising models to black-holes

New methods are presented which enables one to analyze the thermodynamics of systems with long-range interactions. Generically, such systems have entropies which are non-extensive, (do not scale with the size of the system). We show how to calculate the degree of non-extensivity for such a system. We find that a system interacting with a heat reservoir is in a probability distribution of canonical ensembles. The system still possesses a parameter akin to a global temperature, which is constant throughout the substance. There is also a useful quantity which acts like a {\it local temperatures} and it varies throughout the substance. These quantities are closely related to counterparts found in general relativity. A lattice model with long-range spin-spin coupling is studied. This is compared with systems such as those encountered in general relativity, and gravitating systems with Newtonian-type interactions. A long-range lattice model is presented which can be seen as a black-hole analog. One finds that the analog's temperature and entropy have many properties which are found in black-holes. Finally, the entropy scaling behavior of a gravitating perfect fluid of constant density is calculated. For weak interactions, the entropy scales like the volume of the system. As the interactions become stronger, the entropy becomes higher near the surface of the system, and becomes more area-scaling.Comment: Corrects some typos found in published version. Title changed 22 pages, 2 figure

Harrison transformation of hyperelliptic solutions and charged dust disks

We use a Harrison transformation on solutions to the stationary axisymmetric Einstein equations to generate solutions of the Einstein-Maxwell equations. The case of hyperelliptic solutions to the Ernst equation is studied in detail. Analytic expressions for the metric and the multipole moments are obtained. As an example we consider the transformation of a family of counter-rotating dust disks. The resulting solutions can be interpreted as disks with currents and matter with a purely azimuthal pressure or as two streams of freely moving charged particles. We discuss interesting limiting cases as the extreme limit where the charge becomes identical to the mass, and the ultrarelativistic limit where the central redshift diverges.Comment: 20 pages, 9 figure

Counting Domain Walls in N=1 Super Yang-Mills Theory

We study the multiplicity of BPS domain walls in N=1 super Yang-Mills theory, by passing to a weakly coupled Higgs phase through the addition of fundamental matter. The number of domain walls connecting two specified vacuum states is then determined via the Witten index of the induced worldvolume theory, which is invariant under the deformation to the Higgs phase. The worldvolume theory is a sigma model with a Grassmanian target space which arises as the coset associated with the global symmetries broken by the wall solution. Imposing a suitable infrared regulator, the result is found to agree with recent work of Acharya and Vafa in which the walls were realized as wrapped D4-branes in IIA string theory.Comment: 28 pages, RevTeX, 3 figures; v2: discussion of the index slightly expanded, using an alternative regulator, and references added; v3: typos corrected, to appear in Phys. Rev.

Statistics of the gravitational force in various dimensions of space: from Gaussian to Levy laws

We discuss the distribution of the gravitational force created by a Poissonian distribution of field sources (stars, galaxies,...) in different dimensions of space d. In d=3, it is given by a Levy law called the Holtsmark distribution. It presents an algebraic tail for large fluctuations due to the contribution of the nearest neighbor. In d=2, it is given by a marginal Gaussian distribution intermediate between Gaussian and Levy laws. In d=1, it is exactly given by the Bernouilli distribution (for any particle number N) which becomes Gaussian for N>>1. Therefore, the dimension d=2 is critical regarding the statistics of the gravitational force. We generalize these results for inhomogeneous systems with arbitrary power-law density profile and arbitrary power-law force in a d-dimensional universe

Non-thermal dark matter via Affleck-Dine baryogenesis and its detection possibility

The formation and late time decays of Q-balls are generic consequences of the Affleck-Dine (AD) baryogenesis. A substantial amount of the lightest supersymmetry (SUSY) particles (LSPs) are produced non-thermally as the decay products of these Q-balls. This requires a significantly large annihilation cross section of the LSP so as not to overclose the universe, which predicts a higgsino- or wino-like LSP instead of the standard bino LSP. We have reexamined the AD baryogenesis with special attention to the late-time decays of the Q-balls, and then specified the parameter regions where the LSPs produced by the Q-ball decays result in a cosmologically interesting mass density of dark matter by adopting several SUSY breaking models. This reveals new cosmologically interesting parameter regions, which have not attracted much attention so far. We have also investigated the prospects of direct and indirect detection of these dark matter candidates, and found that there is an intriguing possibility to detect them in various next generation dark matter searches.Comment: 51 pages, 18 figures, version accepted for publication in Physical Review

Relic neutrino masses and the highest energy cosmic rays

We consider the possibility that a large fraction of the ultrahigh energy cosmic rays are decay products of Z bosons which were produced in the scattering of ultrahigh energy cosmic neutrinos on cosmological relic neutrinos. We compare the observed ultrahigh energy cosmic ray spectrum with the one predicted in the above Z-burst scenario and determine the required mass of the heaviest relic neutrino as well as the necessary ultrahigh energy cosmic neutrino flux via a maximum likelihood analysis. We show that the value of the neutrino mass obtained in this way is fairly robust against variations in presently unknown quantities, like the amount of neutrino clustering, the universal radio background, and the extragalactic magnetic field, within their anticipated uncertainties. Much stronger systematics arises from different possible assumptions about the diffuse background of ordinary cosmic rays from unresolved astrophysical sources. In the most plausible case that these ordinary cosmic rays are protons of extragalactic origin, one is lead to a required neutrino mass in the range 0.08 eV - 1.3 eV at the 68 % confidence level. This range narrows down considerably if a particular universal radio background is assumed, e.g. to 0.08 eV - 0.40 eV for a large one. The required flux of ultrahigh energy cosmic neutrinos near the resonant energy should be detected in the near future by AMANDA, RICE, and the Pierre Auger Observatory, otherwise the Z-burst scenario will be ruled out.Comment: 19 pages, 22 figures, REVTeX

Mean field effects on the scattered atoms in condensate collisions

We consider the collision of two Bose Einstein condensates at supersonic velocities and focus on the halo of scattered atoms. This halo is the most important feature for experiments and is also an excellent testing ground for various theoretical approaches. In particular we find that the typical reduced Bogoliubov description, commonly used, is often not accurate in the region of parameters where experiments are performed. Surprisingly, besides the halo pair creation terms, one should take into account the evolving mean field of the remaining condensate and on-condensate pair creation. We present examples where the difference is clearly seen, and where the reduced description still holds.Comment: 6 pages, 4 figure

The ANTARES Optical Beacon System

ANTARES is a neutrino telescope being deployed in the Mediterranean Sea. It consists of a three dimensional array of photomultiplier tubes that can detect the Cherenkov light induced by charged particles produced in the interactions of neutrinos with the surrounding medium. High angular resolution can be achieved, in particular when a muon is produced, provided that the Cherenkov photons are detected with sufficient timing precision. Considerations of the intrinsic time uncertainties stemming from the transit time spread in the photomultiplier tubes and the mechanism of transmission of light in sea water lead to the conclusion that a relative time accuracy of the order of 0.5 ns is desirable. Accordingly, different time calibration systems have been developed for the ANTARES telescope. In this article, a system based on Optical Beacons, a set of external and well-controlled pulsed light sources located throughout the detector, is described. This calibration system takes into account the optical properties of sea water, which is used as the detection volume of the ANTARES telescope. The design, tests, construction and first results of the two types of beacons, LED and laser-based, are presented.Comment: 21 pages, 18 figures, submitted to Nucl. Instr. and Meth. Phys. Res.