13,851 research outputs found
Double Well Potential: Perturbation Theory, Tunneling, WKB (beyond instantons)
A simple approximate solution for the quantum-mechanical quartic oscillator
in the double-well regime at arbitrary is
presented. It is based on a combining of perturbation theory near true minima
of the potential, semi-classical approximation at large distances and a
description of tunneling under the barrier. It provides 9-10 significant digits
in energies and gives for wavefunctions the relative deviation in real
-space less than .Comment: 13 pages, invited talk at "Crossing the boundaries: Gauge dynamics at
strong coupling (Shifmania)", Minneapolis, May 14-17, 200
Universal Properties of Two-Dimensional Boson Droplets
We consider a system of N nonrelativistic bosons in two dimensions,
interacting weakly via a short-range attractive potential. We show that for N
large, but below some critical value, the properties of the N-boson bound state
are universal. In particular, the ratio of the binding energies of (N+1)- and
N-boson systems, B_{N+1}/B_N, approaches a finite limit, approximately 8.567,
at large N. We also confirm previous results that the three-body system has
exactly two bound states. We find for the ground state B_3^(0) = 16.522688(1)
B_2 and for the excited state B_3^(1) = 1.2704091(1) B_2.Comment: 4 pages, 2 figures, final versio
Gravitating multidefects from higher dimensions
Warped configurations admitting pairs of gravitating defects are analyzed.
After devising a general method for the construction of multidefects, specific
examples are presented in the case of higher-dimensional Einstein-Hilbert
gravity. The obtained profiles describe diverse physical situations such as
(topological) kink-antikink systems, pairs of non-topological solitons and
bound configurations of a kink and of a non-topological soliton. In all the
mentioned cases the geometry is always well behaved (all relevant curvature
invariants are regular) and tends to five-dimensional anti-de Sitter space-time
for large asymptotic values of the bulk coordinate. Particular classes of
solutions can be generalized to the framework where the gravity part of the
action includes, as a correction, the Euler-Gauss-Bonnet combination. After
scrutinizing the structure of the zero modes, the obtained results are compared
with conventional gravitating configurations containing a single topological
defect.Comment: 27 pages, 5 included figure
Novel Sets of Coupling Expansion Parameters for low-energy pQCD
In quantum theory, physical amplitudes are usually presented in the form of
Feynman perturbation series in powers of coupling constant \al . However, it
is known that these amplitudes are not regular functions at
For QCD, we propose new sets of expansion parameters {\bf w}_k(\as) that
reflect singularity at \as=0 and should be used instead of powers \as^k.
Their explicit form is motivated by the so called Analytic Perturbation Theory.
These parameters reveal saturation in a strong coupling case at the level
\as^{eff}(\as\gg1)={\bf w}_1(\as\gg 1) \sim 0.5 . They can be used for
quanitative analysis of divers low-energy amplitudes.
We argue that this new picture with non-power sets of perturbation expansion
parameters, as well as the saturation feature, is of a rather general nature.Comment: 8 pages, 1 figure, submitted to Part. Nucl. Phys. Let
The Phase Diagram of the Sigma Model
We study the phase diagram of the scalar model in
dimensions. We find that the phase transition is of first order in most of the
parameter space. The theory can still be relevant to continuum physics (as an
effective theory) provided the transition is sufficiently weakly first order.
This places restrictions on the allowed coupling constants.Comment: 3 pages (Latex), 2 eps figures, uses espcrc2.sty, epsf, talk given at
LATTICE9
Comment on "Feynman Effective Classical Potential in the Schrodinger Formulation"
We comment on the paper "Feynman Effective Classical Potential in the
Schrodinger Formulation"[Phys. Rev. Lett. 81, 3303 (1998)]. We show that the
results in this paper about the time evolution of a wave packet in a double
well potential can be properly explained by resorting to a variational
principle for the effective action. A way to improve on these results is also
discussed.Comment: 1 page, 2eps figures, Revte
Meson vacuum phenomenology in a three-flavor linear sigma model with (axial-)vector mesons
We study scalar, pseudoscalar, vector, and axial-vector mesons with
non-strange and strange quantum numbers in the framework of a linear sigma
model with global chiral symmetry. We perform a
global fit of meson masses, decay widths, as well as decay amplitudes. The
quality of the fit is, for a hadronic model that does not consider
isospin-breaking effects, surprisingly good. We also investigate the question
whether the scalar states lie below or above 1 GeV and find the
scalar states above 1 GeV to be preferred as states. Additionally,
we also describe the axial-vector resonances as states.Comment: 29 pages, 4 figures, 3 tables. v2 is the updated version after
referee remarks (dilaton field discussed, a new figure added
Mass of perfect fluid black shells
The spherically symmetric singular perfect fluid shells are considered for
the case of their radii being equal to the event horizon (the black shells). We
study their observable masses, depending at least on the three parameters,
viz., the square speed of sound in the shell, instantaneous radial velocity of
the shell at a moment when it reaches the horizon, and integration constant
related to surface mass density. We discuss the features of black shells
depending on an equation of state.Comment: 1 figure, LaTeX; final version + FA
Quantum Evolution of the Bianchi Type I Model
The behaviour of the flat anisotropic model of the Universe with a scalar
field is explored within the framework of quantum cosmology. The principal
moment of the account of an anisotropy is the presence either negative
potential barrier or positive repelling wall. In the first case occur the above
barrier reflection of the wave function of the Universe, in the second one
there is bounce off a potential wall. The further evolution of the Universe
represents an exponential inflating with fast losses of an anisotropy and
approach to the standard cosmological scenario.Comment: Latex, 18 pages, 5 figure
Spontaneously Broken Spacetime Symmetries and Goldstone's Theorem
Goldstone's theorem states that there is a massless mode for each broken
symmetry generator. It has been known for a long time that the naive
generalization of this counting fails to give the correct number of massless
modes for spontaneously broken spacetime symmetries. We explain how to get the
right count of massless modes in the general case, and discuss examples
involving spontaneously broken Poincare and conformal invariance.Comment: 4 pages; 1 figure; v2: minor corrections. version to appear on PR
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