682 research outputs found
Coupled-mode equations and gap solitons in a two-dimensional nonlinear elliptic problem with a separable periodic potential
We address a two-dimensional nonlinear elliptic problem with a
finite-amplitude periodic potential. For a class of separable symmetric
potentials, we study the bifurcation of the first band gap in the spectrum of
the linear Schr\"{o}dinger operator and the relevant coupled-mode equations to
describe this bifurcation. The coupled-mode equations are derived by the
rigorous analysis based on the Fourier--Bloch decomposition and the Implicit
Function Theorem in the space of bounded continuous functions vanishing at
infinity. Persistence of reversible localized solutions, called gap solitons,
beyond the coupled-mode equations is proved under a non-degeneracy assumption
on the kernel of the linearization operator. Various branches of reversible
localized solutions are classified numerically in the framework of the
coupled-mode equations and convergence of the approximation error is verified.
Error estimates on the time-dependent solutions of the Gross--Pitaevskii
equation and the coupled-mode equations are obtained for a finite-time
interval.Comment: 32 pages, 16 figure
Phases of \Nc= \infty QCD-like gauge theories on and nonperturbative orbifold-orientifold equivalences
We study the phase diagrams of \Nc= \infty vector-like, asymptotically free
gauge theories as a function of volume, on . The theories of
interest are the ones with fermions in two index representations [adjoint,
(anti)symmetric, and bifundamental abbreviated as QCD(adj), QCD(AS/S) and
QCD(BF)], and are interrelated via orbifold or orientifold projections. The
phase diagrams reveal interesting phenomena such as disentangled realizations
of chiral and center symmetry, confinement without chiral symmetry breaking,
zero temperature chiral transitions, and in some cases, exotic phases which
spontaneously break the discrete symmetries such as C, P, T as well as CPT. In
a regime where the theories are perturbative, the deconfinement temperature in
SYM, and QCD(AS/S/BF) coincide. The thermal phase diagrams of thermal orbifold
QCD(BF), orientifold QCD(AS/S), and SYM coincide, provided charge
conjugation symmetry for QCD(AS/S) and interchange symmetry of the
QCD(BF) are not broken in the phase continously connected to limit. When
the circle is endowed with periodic boundary conditions, the (nonthermal)
phase diagrams of orbifold and orientifold QCD are still the same, however,
both theories possess chirally symmetric phases which are absent in \None
SYM. The match and mismatch of the phase diagrams depending on the spin
structure of fermions along the circle is naturally explained in terms of
the necessary and sufficient symmetry realization conditions which determine
the validity of the nonperturbative orbifold orientifold equivalence.Comment: 60 pages, 6 figure
Spectrum of the Dirac Operator and Multigrid Algorithm with Dynamical Staggered Fermions
Complete spectra of the staggered Dirac operator \Dirac are determined in
quenched four-dimensional gauge fields, and also in the presence of
dynamical fermions.
Periodic as well as antiperiodic boundary conditions are used.
An attempt is made to relate the performance of multigrid (MG) and conjugate
gradient (CG) algorithms for propagators with the distribution of the
eigenvalues of~\Dirac.
The convergence of the CG algorithm is determined only by the condition
number~ and by the lattice size.
Since~'s do not vary significantly when quarks become dynamic,
CG convergence in unquenched fields can be predicted from quenched
simulations.
On the other hand, MG convergence is not affected by~ but depends on
the spectrum in a more subtle way.Comment: 19 pages, 8 figures, HUB-IEP-94/12 and KL-TH 19/94; comes as a
uuencoded tar-compressed .ps-fil
Interface free-energy exponent in the one-dimensional Ising spin glass with long-range interactions in both the droplet and broken replica symmetry regions
The one-dimensional Ising spin-glass model with power-law long-range
interactions is a useful proxy model for studying spin glasses in higher space
dimensions and for finding the dimension at which the spin-glass state changes
from having broken replica symmetry to that of droplet behavior. To this end we
have calculated the exponent that describes the difference in free energy
between periodic and antiperiodic boundary conditions. Numerical work is done
to support some of the assumptions made in the calculations and to determine
the behavior of the interface free-energy exponent of the power law of the
interactions. Our numerical results for the interface free-energy exponent are
badly affected by finite-size problems.Comment: 10 pages, 5 figures, 3 table
Periodic solutions and torsional instability in a nonlinear nonlocal plate equation
A thin and narrow rectangular plate having the two short edges hinged and the
two long edges free is considered. A nonlinear nonlocal evolution equation
describing the deformation of the plate is introduced: well-posedness and
existence of periodic solutions are proved. The natural phase space is a
particular second order Sobolev space that can be orthogonally split into two
subspaces containing, respectively, the longitudinal and the torsional
movements of the plate. Sufficient conditions for the stability of periodic
solutions and of solutions having only a longitudinal component are given. A
stability analysis of the so-called prevailing mode is also performed. Some
numerical experiments show that instabilities may occur. This plate can be seen
as a simplified and qualitative model for the deck of a suspension bridge,
which does not take into account the complex interactions between all the
components of a real bridge.Comment: 34 pages, 4 figures. The result of Theorem 6 is correct, but the
proof was not correct. We slightly changed the proof in this updated versio
DOMAIN WALLS IN THE QUANTUM TRANSVERSE ISING MODEL
We discuss several problems concerning domain walls in the spin Ising
model at zero temperature in a magnetic field, , applied in the
direction. Some results are also given for the planar (-) model in a
transverse field. We treat the quantum problem in one dimension by perturbation
theory at small and numerically over a large range of . We obtain the
spin density profile by fixing the spins at opposite ends of the chain to have
opposite signs of . One dimension is special in that there the quantum
width of the wall is proportional to the size of the system. We also study
the quantitative features of the `particle' band which extends up to energies
of order above the ground state. Except for the planar limit, this particle
band is well separated from excitations having energy involving creation
of more walls. At large this particle band develops energy gaps and the
lowest sub-band has tunnel splittings of order . This scale of
energy gives rise to anomalous scaling with respect to a) finite size, b)
temperature, or c) random potentials. The intrinsic width of the domain wall
and the pinning energy are also defined and calculated in certain limiting
cases. The general conclusion is that quantum effects prevent the wall from
being sharp and in higher dimension would prevent sudden excursions in the
configuration of the wall.Comment: 40 pages and 13 figures, Phys. Rev. B, to be publishe
Truncated Hilbert space approach to the 2d theory
We apply the massive analogue of the truncated conformal space approach to
study the two dimensional theory in finite volume. We focus on the
broken phase and determine the finite size spectrum of the model numerically.
We interpret the results in terms of the Bethe-Yang spectrum, from which we
extract the infinite volume masses and scattering matrices for various
couplings. We compare these results against semiclassical analysis and
perturbation theory. We also analyze the critical point of the model and
confirm that it is in the Ising universality class.Comment: pdflatex, 35 pages with 29 pdf figures. Binary program is also
attached, run on linux as: phi4 config.dat, v2: typos corrected, comparison
to other works and references added, vacuum splitting analysis corrected,
comparison to sine-Gordon TCSA added, v3: improved numerics, analysis on
excited kink added, critical point investigate
Polyakov Loop Dynamics in the Center Symmetric Phase
A study of the center symmetric phase of SU(2) Yang Mills theory is
presented. Realization of the center symmetry is shown to result from
non-perturbative gauge fixing. Dictated by the center symmetry, this phase
exhibits already at the perturbative level confinement like properties. The
analysis is performed by investigating the dynamics of the Polyakov loops. The
ultralocality of these degrees of freedom implies significant changes in the
vacuum structure of the theory. General properties of the confined phase and of
the transition to the deconfined phase are discussed. Perturbation theory built
upon the vacuum of ultralocal Polyakov loops is presented and used to
calculate, via the Polyakov loop correlator, the static quark-antiquark
potential.Comment: 45 pages, LaTeX, 8 figure
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