102 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, .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 and zero temperature in spaces with nontrivial
topology of the form and . 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 ,
where is the length of the circumference . Moreover, it is shown that
at some finite values of the superconducting phase transition is shifted to
smaller values both of and particle density in comparison with the case
of .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
spacetime with compactified space coordinate are investigated
in the presence of the isospin chemical potential . The consideration is
performed in the limit , i.e. in the case with infinite number of
colored quarks. It is shown that at ( is the length of the
circumference ) the pion condensation phase is realized for arbitrary
small nonzero . At finite values of , the phase portraits of the
model in terms of parameters and are obtained
both for periodic and antiperiodic boundary conditions of the quark field. It
turns out that in the plane there is a strip
which lies as a whole inside the pion condensed phase.
In this phase the pion condensation gap is an oscillating function vs both
(at fixed ) and (at fixed ).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 - and color
chemical potential. It was found out that in the color superconducting (2SC)
phase, i.e. at MeV, aquires rather small values
10 MeV in order to ensure the color neutrality. In this phase the - and
meson masses are evaluated around 330 MeV. The spectrum of
scalar diquarks in the color neutral 2SC phase consists of a heavy (-singlet) resonance with mass 1100 MeV, four light diquarks with
mass , 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 , a mass splitting
of scalar diquarks and antidiquarks is shown to arise if , contrary
to the case of , where the masses of scalar antidiquarks and diquarks
are degenerate at the value ~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
Magnetic Oscillations in Dense Cold Quark Matter with Four-Fermion Interactions
The phase structures of Nambu-Jona-Lasinio models with one or two flavours
have been investigated at non-zero values of and , where is an
external magnetic field and is the chemical potential. In the phase
portraits of both models there arise infinitely many massless chirally
symmetric phases, as well as massive ones with spontaneously broken chiral
invariance, reflecting the existence of infinitely many Landau levels. Phase
transitions of first and second orders and a lot of tricritical points have
been shown to exist in phase diagrams. In the massless case, such a phase
structure leads unavoidably to the standard van Alphen-de Haas magnetic
oscillations of some thermodynamical quantities, including magnetization,
pressure and particle density. In the massive case we have found an oscillating
behaviour not only for thermodynamical quantities, but also for a dynamical
quantity as the quark mass. Besides, in this case we have non-standard, i.e.
non-periodic, magnetic oscillations, since the frequency of oscillations is an
-dependent quantity.Comment: latex, 29 pages, 8 figure
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