94 research outputs found

### Curvature and topological effects on dynamical symmetry breaking in a four- and eight-fermion interaction model

A dynamical mechanism for symmetry breaking is investigated under the
circumstances with the finite curvature, finite size and non-trivial topology.
A four- and eight-fermion interaction model is considered as a prototype model
which induces symmetry breaking at GUT era. Evaluating the effective potential
in the leading order of the 1/N-expansion by using the dimensional
regularization, we explicitly calculate the phase boundary which divides the
symmetric and the broken phase in a weakly curved space-time and a flat
space-time with non-trivial topology, $R^{D-1} \otimes S^1$.Comment: 20 pages, 21 figure

### Cooper pairing and finite-size effects in a NJL-type four-fermion model

Starting from a NJL-type model with N fermion species fermion and difermion
condensates and their associated phase structures are considered at nonzero
chemical potential $\mu$ and zero temperature in spaces with nontrivial
topology of the form $S^1\otimes S^1\otimes S^1$ and $R^2\otimes S^1$. Special
attention is devoted to the generation of the superconducting phase. In
particular, for the cases of antiperiodic and periodic boundary conditions we
have found that the critical curve of the phase transitions between the chiral
symmetry breaking and superconducting phases as well as the corresponding
condensates and particle densities strongly oscillate vs $\lambda\sim 1/L$,
where $L$ is the length of the circumference $S^1$. Moreover, it is shown that
at some finite values of $L$ the superconducting phase transition is shifted to
smaller values both of $\mu$ and particle density in comparison with the case
of $L=\infty$.Comment: 13 pages, 13 figures; minor changes; new references added; version
accepted to PR

### Finite size effects in the Gross-Neveu model with isospin chemical potential

The properties of the two-flavored Gross-Neveu model in the (1+1)-dimensional
$R^1\times S^1$ spacetime with compactified space coordinate are investigated
in the presence of the isospin chemical potential $\mu_I$. The consideration is
performed in the limit $N_c\to\infty$, i.e. in the case with infinite number of
colored quarks. It is shown that at $L=\infty$ ($L$ is the length of the
circumference $S^1$) the pion condensation phase is realized for arbitrary
small nonzero $\mu_I$. At finite values of $L$, the phase portraits of the
model in terms of parameters $\nu\sim\mu_I$ and $\lambda\sim 1/L$ are obtained
both for periodic and antiperiodic boundary conditions of the quark field. It
turns out that in the plane $(\lambda,\nu)$ there is a strip
$0\le\lambda<\lambda_c$ which lies as a whole inside the pion condensed phase.
In this phase the pion condensation gap is an oscillating function vs both
$\lambda$ (at fixed $\nu$) and $\nu$ (at fixed $\lambda$).Comment: 12 pages, 8 figures; one reference added; accepted for publication in
PR

### Algebraic approach to the spectral problem for the Schroedinger equation with power potentials

The method reducing the solution of the Schroedinger equation for several
types of power potentials to the solution of the eigenvalue problem for the
infinite system of algebraic equations is developed. The finite truncation of
this system provides high accuracy results for low-lying levels. The proposed
approach is appropriate both for analytic calculations and for numerical
computations. This method allows also to determine the spectrum of the
Schroedinger-like relativistic equations. The heavy quarkonium (charmonium and
bottomonium) mass spectra for the Cornell potential and the sum of the Coulomb
and oscillator potentials are calculated. The results are in good agreement
with experimental data.Comment: 17 pages, including 6 PostScript figures (epsf style

### Mesons and diquarks in the color neutral 2SC phase of dense cold quark matter

The spectrum of meson and diquark excitations of dense color neutral cold
quark matter is investigated in the framework of a 2-flavored
Nambu--Jona-Lasinio type model, including a quark $\mu$- and color $\mu_8$
chemical potential. It was found out that in the color superconducting (2SC)
phase, i.e. at $\mu>\mu_c=342$ MeV, $\mu_8$ aquires rather small values $\sim$
10 MeV in order to ensure the color neutrality. In this phase the $\pi$- and
$\sigma$ meson masses are evaluated around $\sim$ 330 MeV. The spectrum of
scalar diquarks in the color neutral 2SC phase consists of a heavy ($\rm
SU_c(2)$-singlet) resonance with mass $\sim$ 1100 MeV, four light diquarks with
mass $3|\mu_8|$, and one Nambu --Goldstone boson which is in accordance with
the Goldstone theorem. Moreover, in the 2SC phase there are five light stable
particles as well as a heavy resonance in the spectrum of pseudo-scalar
diquarks. In the color symmetric phase, i.e. for $\mu <\mu_c$, a mass splitting
of scalar diquarks and antidiquarks is shown to arise if $\mu\ne 0$, contrary
to the case of $\mu = 0$, where the masses of scalar antidiquarks and diquarks
are degenerate at the value $\sim$~700 MeV. If the coupling strength in the
pseudo-scalar diquark channel is the same as in the scalar diquark one (as for
QCD-inspired NJL models), then in the color symmetric phase pseudo-scalar
diquarks are not allowed to exist as stable particles.Comment: 18 pages, 4 figures; version accepted for the publication in PR

### Chiral phase transitions in strong chromomagnetic fields at finite temperature and dimensional reduction

Dynamical fermion mass generation in external chromomagnetic fields is
considered at non--zero temperature. The general features of dynamical chiral
symmetry breaking ($D\chi SB$) are investigated for several field
configurations in relation to their symmetry properties and the form of the
quark spectrum. According to the fields, there arises dimensional reduction by
one or two units. In all cases there exists $D\chi SB$ even at weak quark
attraction, confirming the idea about the dimensional insensitivity of this
mechanism in a chromomagnetic field.Comment: LATEX file, 12 pages, no figure

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