1,261 research outputs found
Diquark and Pion Condensation in Random Matrix Models for two-color QCD
We introduce a random matrix model with the symmetries of QCD with two colors
at nonzero isospin and baryon chemical potentials and temperature. We analyze
its phase diagram and find phases with condensation of pion and diquark states
in addition to the phases with spontaneously broken chiral symmetries. In the
limit of small chemical potentials and quark masses, we reproduce the mean
field results obtained from chiral Lagrangians. As in the case of QCD with
three colors, the presence of two chemical potentials breaks the flavor
symmetry and leads to phases that are characterized by different behaviors of
the chiral condensates for each flavor. In particular, the phase diagram we
obtain is similar to QCD with three colors and three flavors of quarks of equal
masses at zero baryon chemical potential and nonzero isospin and strange
chemical potentials. A tricritical point of the superfluid transitions found in
lattice calculations and from an analysis in terms of chiral Lagrangians does
not appear in the random matrix model. Remarkably, at fixed isospin chemical
potential, for the regions outside of the superfluid phases, the phase diagram
in the temperature - baryon chemical potential plane for two colors and three
colors are qualitatively the same.Comment: 19 pages, 7 figures, RevTeX
Yang-Mills Theory on a Cylinder Coupled to Point Particles
We study a model of quantum Yang-Mills theory with a finite number of gauge
invariant degrees of freedom. The gauge field has only a finite number of
degrees of freedom since we assume that space-time is a two dimensional
cylinder. We couple the gauge field to matter, modeled by either one or two
nonrelativistic point particles. These problems can be solved {\it without any
gauge fixing}, by generalizing the canonical quantization methods of
Ref.\[rajeev] to the case including matter. For this, we make use of the
geometry of the space of connections, which has the structure of a Principal
Fiber Bundle with an infinite dimensional fiber. We are able to reduce both
problems to finite dimensional, exactly solvable, quantum mechanics problems.
In the case of one particle, we find that the ground state energy will diverge
in the limit of infinite radius of space, consistent with confinement. In the
case of two particles, this does not happen if they can form a color singlet
bound state (`meson').Comment: 37 pages, UR-1327 ER-40685-77
Effective-range approach and scaling laws for electromagnetic strength in neutron-halo nuclei
We study low-lying multipole strength in neutron-halo nuclei. The strength
depends only on a few low-energy constants: the neutron separation energy, the
asymptotic normalization coefficient of the bound state wave function, and the
scattering length that contains the information on the interaction in the
continuum. The shape of the transition probability shows a characteristic
dependence on few scaling parameters and the angular momenta. The total E1
strength is related to the root-mean-square radius of the neutron wave function
in the ground state and shows corresponding scaling properties. We apply our
approach to the E1 strength distribution of 11Be.Comment: 4 pages, 1 figure (modified), additional table, extended discussion
of example, accepted for publication in Phys. Rev. Let
The Ferromagnetic Potts model under an external magnetic field: an exact renormalization group approach
The q-state ferromagnetic Potts model under a non-zero magnetic field coupled
with the 0^th Potts state was investigated by an exact real-space
renormalization group approach. The model was defined on a family of diamond
hierarchical lattices of several fractal dimensions d_F. On these lattices, the
renormalization group transformations became exact for such a model when a
correlation coupling that singles out the 0^th Potts state was included in the
Hamiltonian. The rich criticality presented by the model with q=3 and d_F=2 was
fully analyzed. Apart from the Potts criticality for the zero field, an
Ising-like phase transition was found whenever the system was submitted to a
strong reverse magnetic field. Unusual characteristics such as cusps and
dimensional reduction were observed on the critical surface.Comment: 8 pages, 6 figures. Accepted to be published in Phys. Rev B (2006
Renormalization Group Approach to Strong-Coupled Superconductors
We develop an asymptotically exact renormalization group (RG) approach that
treats electron-electron and electron-phonon interactions on equal footing. The
approach allows an unbiased study of the instabilities of Fermi liquids without
the assumption of a broken symmetry. We apply our method to the problem of
strongly coupled superconductors and find the temperature T* below which the
high-temperature Fermi liquid state becomes unstable towards Cooper pairing. We
show that T* is the same as the critical temperature Tc obtained in
Eliashberg's strong coupling theory starting from the low-temperature
superconducting phase. We also show that Migdal's theorem is implicit in our
approach. Finally, our results lead to a novel way to calculate numerically,
from microscopic parameters, the transition temperature of superconductors.Comment: 6 pages, 3 figures, expanded presentation, final versio
Magnetic models on Apollonian networks
Thermodynamic and magnetic properties of Ising models defined on the
triangular Apollonian network are investigated. This and other similar networks
are inspired by the problem of covering an Euclidian domain with circles of
maximal radii. Maps for the thermodynamic functions in two subsequent
generations of the construction of the network are obtained by formulating the
problem in terms of transfer matrices. Numerical iteration of this set of maps
leads to exact values for the thermodynamic properties of the model. Different
choices for the coupling constants between only nearest neighbors along the
lattice are taken into account. For both ferromagnetic and anti-ferromagnetic
constants, long range magnetic ordering is obtained. With exception of a size
dependent effective critical behavior of the correlation length, no evidence of
asymptotic criticality was detected.Comment: 21 pages, 5 figure
Further evidence for linearly-dispersive Cooper pairs
A recent Bose-Einstein condensation (BEC) model of several cuprate
superconductors is based on bosonic Cooper pairs (CPs) moving in 3D with a
quadratic energy-momentum (dispersion) relation. The 3D BEC condensate-fraction
vs. temperature (T/Tc, where Tc is the BEC transition temperature) formula
poorly fits penetration-depth data for two cuprates in the range (1/2, 1]. We
show how these fits are dramatically improved assuming cuprates to be quasi-2D,
and how equally good fits obtain for conventional 3D and quasi-1D nanotube
superconducting data, provided the correct CP dispersion is assumed in BEC at
their assumed corresponding dimensionalities. This is offered as additional
concrete empirical evidence for linearly-dispersive pairs in another recent BEC
scenario of superconductors within which a BCS condensate turns out to be a
very special case.Comment: 9 pages, 1 figur
Physics of -Meson Condensation and High Temperature Cuprate Superconductors
The idea of condensation of the Goldstone -meson field in nuclear matter
had been put forward a long time ago. However, it was established that the
normal nuclear density is too low, it is not sufficient to condensate
-mesons. This is why the -condensation has never been observed.
Recent experimental and theoretical studies of high temperature cuprate
superconductors have revealed condensation of Goldstone magnons, the effect
fully analogous to the -condensation. The magnon condensation has been
observed. It is clear now that quantum fluctuations play a crucial role in the
condensation, in particular they drive a quantum phase transition that destroys
the condensate at some density of fermions
Phase Separation and Charge-Ordered Phases of the d = 3 Falicov-Kimball Model at T>0: Temperature-Density-Chemical Potential Global Phase Diagram from Renormalization-Group Theory
The global phase diagram of the spinless Falicov-Kimball model in d = 3
spatial dimensions is obtained by renormalization-group theory. This global
phase diagram exhibits five distinct phases. Four of these phases are
charge-ordered (CO) phases, in which the system forms two sublattices with
different electron densities. The CO phases occur at and near half filling of
the conduction electrons for the entire range of localized electron densities.
The phase boundaries are second order, except for the intermediate and large
interaction regimes, where a first-order phase boundary occurs in the central
region of the phase diagram, resulting in phase coexistence at and near half
filling of both localized and conduction electrons. These two-phase or
three-phase coexistence regions are between different charge-ordered phases,
between charge-ordered and disordered phases, and between dense and dilute
disordered phases. The second-order phase boundaries terminate on the
first-order phase transitions via critical endpoints and double critical
endpoints. The first-order phase boundary is delimited by critical points. The
cross-sections of the global phase diagram with respect to the chemical
potentials and densities of the localized and conduction electrons, at all
representative interactions strengths, hopping strengths, and temperatures, are
calculated and exhibit ten distinct topologies.Comment: Calculated density phase diagrams. Added discussions and references.
14 pages, 9 figures, 4 table
Pion parameters in nuclear medium from chiral perturbation theory and virial expansion
We consider two methods to find the effective parameters of the pion
traversing a nuclear medium. One is the first order chiral perturbation
theoretic evaluation of the pion pole contribution to the two-point function of
the axial-vector current. The other is the exact, first order virial expansion
of the pion self-energy. We find that, although the results of chiral
perturbation theory are not valid at normal nuclear density, those from the
virial expansion may be reliable at such density. The latter predicts both the
mass-shift and the in-medium decay width of the pion to be small, of about a
few MeV.Comment: 9 Pages RevTex, 3 eps figure
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