12,994 research outputs found
Microscopic spectral density in random matrix models for chiral and diquark condensation
We examine random matrix models of QCD which are capable of supporting both
chiral and diquark condensation. A numerical study of the spectral densities
near zero virtuality shows that the introduction of color in the interactions
does not alter the one-body results imposed by chiral symmetry. A model with
three colors has the spectral density predicted for the chiral ensemble with a
Dyson index beta = 2; a pseudoreal model with two colors exhibits the spectral
density of the chiral ensemble with beta = 1.Comment: 6 pages, 3 eps figures, uses revtex4 and graphicx. v2 : minor
editions, Fig. 3 shows relative deviations rather than absolute. Version to
appear in PR
Random matrix models for chiral and diquark condensation
We consider random matrix models for the thermodynamic competition between
chiral symmetry breaking and diquark condensation in QCD at finite temperature
and finite baryon density. The models produce mean field phase diagrams whose
topology depends solely on the global symmetries of the theory. We discuss the
block structure of the interactions that is imposed by chiral, spin, and color
degrees of freedom and comment on the treatment of density and temperature
effects. Extension of the coupling parameters to a larger class of theories
allows us to investigate the robustness of the phase topology with respect to
variations in the dynamics of the interactions. We briefly study the phase
structure as a function of coupling parameters and the number of colors.Comment: 6 pages, 2 figures, proceedings of the workshop "Three Days of
Hadronic Physics", Joint Meeting Heidelberg-Liege-Paris-Rostock,
16/12/2004-18/12/2004, Sol Cress, Spa, Belgium. v2: typographical errors
corrected in reference
Random matrix model for antiferromagnetism and superconductivity on a two-dimensional lattice
We suggest a new mean field method for studying the thermodynamic competition
between magnetic and superconducting phases in a two-dimensional square
lattice. A partition function is constructed by writing microscopic
interactions that describe the exchange of density and spin-fluctuations. A
block structure dictated by spin, time-reversal, and bipartite symmetries is
imposed on the single-particle Hamiltonian. The detailed dynamics of the
interactions are neglected and replaced by a normal distribution of random
matrix elements. The resulting partition function can be calculated exactly.
The thermodynamic potential has a structure which depends only on the spectrum
of quasiparticles propagating in fixed condensation fields, with coupling
constants that can be related directly to the variances of the microscopic
processes. The resulting phase diagram reveals a fixed number of phase
topologies whose realizations depend on a single coupling-parameter ratio,
alpha. Most phase topologies are realized for a broad range of values of alpha
and can thus be considered robust with respect to moderate variations in the
detailed description of the underlying interactions.Comment: 21 pages, 8 figures, RevTex 4. Minor grammatical errors corrected in
the last versio
The Euler--Poisson system in 2D: global stability of the constant equilibrium solution
We consider the (repulsive) Euler-Poisson system for the electrons in two
dimensions and prove that small smooth perturbations of a constant background
exist for all time and remain smooth (never develop shocks). This extends to 2D
the work of Guo.Comment: 39 page
The Euler--Maxwell system for electrons: global solutions in
A basic model for describing plasma dynamics is given by the Euler-Maxwell
system, in which compressible ion and electron fluids interact with their own
self-consistent electromagnetic field. In this paper we consider the
"one-fluid" Euler--Maxwell model for electrons, in 2 spatial dimensions, and
prove global stability of a constant neutral background.Comment: Revised versio
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