Relativistic harmonic oscillator model for quark stars

The relativistic harmonic oscillator (RHO) model of hadrons is used to study quark stars. The mass-radius relationship is obtained and compared with bag model of quark star, using Tolman-Oppenheimer-Volkoff equation. In this model, the outward degenerate pressure due to discrete Landau levels and Landau degeneracy balances the inward gravitational pressure. Where as in bag model the degenerate pressure is due to the standard continuum levels which balances the combined inward pressure due to gravitation and bag pressure. So in RHO model, the confinement effect is included in the degenerate pressure. We found a qualitative similarity, but quantitative differences in mass-radius relationship of quark stars in these two models. Masses and radii are relatively larger and the central energy densities, required for stable quark stars, are lower in RHO model than that of bag model.Comment: 7 pages, 1 figure, articl

Theory of cooling by flow through narrow pores

We consider the possibility of adding a stage to a dilution refrigerator to provide additional cooling by ``filtering out'' hot atoms. Three methods are considered: 1) Effusion, where holes having diameters larger than a mean-free path allow atoms to pass through easily; 2) Particle waveguide-like motion using very narrow channels that greatly restrict the quantum states of the atoms in a channel. 3) Wall-limited diffusion through channels, in which the wall scattering is disordered so that local density equilibrium is established in a channel. We assume that channel dimension are smaller than the mean-free path for atom-atom interactions. The particle waveguide and the wall-limited diffusion methods using channels on order of the de Broglie wavelength give cooling. Recent advances in nano-filters give this method some hope of being practical.Comment: 10 pages, 3 figures. Corrected typos and made some minor wording change

Single parameter quasi-particle model for QGP

We discuss a new single parameter quasi-particle model and study the thermodynamics of (2+1)-flavor quark gluon plasma (QGP). Our model with a single parameter explains remarkably well the lattice simulation results of Fodor et. al. Phys. Lett. B568, 73 (2003).Comment: 9 pages, 3 figures, articl

A Model for Phase Transition based on Statistical Disassembly of Nuclei at Intermediate Energies

Consider a model of particles (nucleons) which has a two-body interaction which leads to bound composites with saturation properties. These properties are : all composites have the same density and the ground state energies of composites with k nucleons are given by -kW+\sigma k^{2/3} where W and \sigma are positive constants. W represents a volume term and \sigma a surface tension term. These values are taken from nuclear physics. We show that in the large N limit where N is the number of particles such an assembly in a large enclosure at finite temperature shows properties of liquid-gas phase transition. We do not use the two-body interaction but the gross properties of the composites only. We show that (a) the p-\rho isotherms show a region where pressure does not change as $\rho$ changes just as in Maxwell construction of a Van der Waals gas, (b) in this region the chemical potential does not change and (c) the model obeys the celebrated Clausius-Clapeyron relations. A scaling law for the yields of composites emerges. For a finite number of particles N (upto some thousands) the problem can be easily solved on a computer. This allows us to study finite particle number effects which modify phase transition effects. The model is calculationally simple. Monte-Carlo simulations are not needed.Comment: RevTex file, 21 pages, 5 figure

Dynamical instability of a spin spiral in an interacting Fermi gas as a probe of the Stoner transition

We propose an experiment to probe ferromagnetic phenomena in an ultracold Fermi gas, while alleviating the sensitivity to three-body loss and competing many-body instabilities. The system is initialized in a small pitch spin spiral, which becomes unstable in the presence of repulsive interactions. To linear order the exponentially growing collective modes exhibit critical slowing down close to the Stoner transition point. Also, to this order, the dynamics are identical on the paramagnetic and ferromagnetic sides of the transition. However, we show that scattering off the exponentially growing modes qualitatively alters the collective mode structure. The critical slowing down is eliminated and in its place a new unstable branch develops at large wave vectors. Furthermore, long-wavelength instabilities are quenched on the paramagnetic side of the transition. We study the experimental observation of the instabilities, specifically addressing the trapping geometry and how phase-contrast imaging will reveal the emerging domain structure. These probes of the dynamical phenomena could allow experiments to detect the transition point and distinguish between the paramagnetic and ferromagnetic regimes

Bose-Einstein Condensation in the Relativistic Ideal Bose Gas

The Bose-Einstein condensation (BEC) critical temperature in a relativistic ideal Bose gas of identical bosons, with and without the antibosons expected to be pair-produced abundantly at sufficiently hot temperatures, is exactly calculated for all boson number-densities, all boson point rest masses, and all temperatures. The Helmholtz free energy at the critical BEC temperature is found to be lower, thus implying that the omission of antibosons always leads to the computation of a metastable state.Comment: 10 pages, 4 figure

Feshbach Resonances and Limiting Thermodynamics of Strongly Correlated Nucleons

A finite temperature model of strongly correlated nucleons with underlying isospin symmetries is developed. The model can be used to study the role of bound states and Feshbach resonances on the thermal properties of a spin 1/2, isospin 1/2 system of protons and neutrons by varying the proton fraction. An analysis of features associated with a universal thermodynamic limit or unitary limit is given. In the limit of very large scattering length, the effective range to quantum thermal wavelength appears as a limiting scale in an interaction energy and equation of state.Comment: 8 pages, 4 figure

Statistical Mechanics and Lorentz Violation

The theory of statistical mechanics is studied in the presence of Lorentz-violating background fields. The analysis is performed using the Standard-Model Extension (SME) together with a Jaynesian formulation of statistical inference. Conventional laws of thermodynamics are obtained in the presence of a perturbed hamiltonian that contains the Lorentz violating terms. As an example, properties of the nonrelativistic ideal gas are calculated in detail. To lowest order in Lorentz violation, the scalar thermodynamic variables are only corrected by a rotationally invariant combination of parameters that mimics a (frame dependent) effective mass. Spin couplings can induce a temperature independent polarization in the classical gas that is not present in the conventional case. Precision measurements in the residual expectation values of the magnetic moment of Fermi gases in the limit of high temperature may provide interesting limits on these parameters.Comment: 7 pages, revte

Dirac particle in a spherical scalar potential well

In this paper we investigate a solution of the Dirac equation for a spin-$\frac{1}2$ particle in a scalar potential well with full spherical symmetry. The energy eigenvalues for the quark particle in $s_{1/2}$ states (with $\kappa=-1$) and $p_{1/2}$ states (with $\kappa=1$) are calculated. We also study the continuous Dirac wave function for a quark in such a potential, which is not necessarily infinite. Our results, at infinite limit, are in good agreement with the MIT bag model. We make some remarks about the sharpness value of the wave function on the wall. This model, for finite values of potential, also could serve as an effective model for the nucleus where $U(r)$ is the effective single particle potential.Comment: 9 pages, 8 figures, revtex4, version to appear in PR

Thermodynamics of a model for RNA folding

We analyze the thermodynamic properties of a simplified model for folded RNA molecules recently studied by G. Vernizzi, H. Orland, A. Zee (in {\it Phys. Rev. Lett.} {\bf 94} (2005) 168103). The model consists of a chain of one-flavor base molecules with a flexible backbone and all possible pairing interactions equally allowed. The spatial pseudoknot structure of the model can be efficiently studied by introducing a $N \times N$ hermitian random matrix model at each chain site, and associating Feynman diagrams of these models to spatial configurations of the molecules. We obtain an exact expression for the topological expansion of the partition function of the system. We calculate exact and asymptotic expressions for the free energy, specific heat, entanglement and chemical potential and study their behavior as a function of temperature. Our results are consistent with the interpretation of $1/N$ as being a measure of the concentration of $\rm{Mg}^{++}$ in solution.Comment: 11 pages, 4 figure