4,265 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
Asymptotic Freedom of Elastic Strings and Barriers
We study the problem of a quantized elastic string in the presence of an
impenetrable wall. This is a two-dimensional field theory of an N-component
real scalar field which becomes interacting through the restriction that
the magnitude of is less than , for a spherical wall of
radius . The N=1 case is a string vibrating in a plane between
two straight walls. We review a simple nonperturbative argument that there is a
gap in the spectrum, with asymptotically-free behavior in the coupling (which
is the reciprocal of ) for N greater than or equal to one. This
scaling behavior of the mass gap has been disputed in some of the recent
literature. We find, however, that perturbation theory and the 1/N expansion
each confirms that these theories are asymptotically free. The large N limit
coincides with that of the O(N) nonlinear sigma model. A theta parameter exists
for the N=2 model, which describes a string confined to the interior of a
cylinder of radius .Comment: Text slightly improved, bibilography corrected, more typos corrected,
still Latex 7 page
't Hooft-Polyakov monopoles in lattice SU(N)+adjoint Higgs theory
We investigate twisted C-periodic boundary conditions in SU(N) gauge field
theory with an adjoint Higgs field. We show that with a suitable twist for even
N one can impose a non-zero magnetic charge relative to residual U(1) gauge
groups in the broken phase, thereby creating a 't Hooft-Polyakov magnetic
monopole. This makes it possible to use lattice Monte-Carlo simulations to
study the properties of these monopoles in the quantum theory.Comment: 15 pages, 6 figure
Models at a Lifshitz Point
We consider models in dimensions around Lifshitz fixed
points with dynamical critical exponent , in the large-N expansion. It is
shown that these models are asymptotically free and dynamically generate a mass
for the fields for all . We demonstrate that, for , the
initially nondynamical gauge field acquires kinetic terms in a way similar to
usual models in 1+1 dimensions. Lorentz invariance emerges
generically in the low-energy electrodynamics, with a nontrivial dielectric
constant given by the inverse mass gap and a magnetic permeability which has a
logarithmic dependence on scale. At a special multicritical point, the
low-energy electrodynamics also has , and an essentially singular
dependence of the effective action on .Comment: LaTeX 13 pages; added a comment about constant field effective
action. version published in Physical Review
Adsorption and desorption of hydrogen at nonpolar GaN(1-100) surfaces: Kinetics and impact on surface vibrational and electronic properties
The adsorption of hydrogen at nonpolar GaN(1-100) surfaces and its impact on
the electronic and vibrational properties is investigated using surface
electron spectroscopy in combination with density functional theory (DFT)
calculations. For the surface mediated dissociation of H2 and the subsequent
adsorption of H, an energy barrier of 0.55 eV has to be overcome. The
calculated kinetic surface phase diagram indicates that the reaction is
kinetically hindered at low pressures and low temperatures. At higher
temperatures ab-initio thermodynamics show, that the H-free surface is
energetically favored. To validate these theoretical predictions experiments at
room temperature and under ultrahigh vacuum conditions were performed. They
reveal that molecular hydrogen does not dissociatively adsorb at the GaN(1-100)
surface. Only activated atomic hydrogen atoms attach to the surface. At
temperatures above 820 K, the attached hydrogen gets desorbed. The adsorbed
hydrogen atoms saturate the dangling bonds of the gallium and nitrogen surface
atoms and result in an inversion of the Ga-N surface dimer buckling. The
signatures of the Ga-H and N-H vibrational modes on the H-covered surface have
experimentally been identified and are in good agreement with the DFT
calculations of the surface phonon modes. Both theory and experiment show that
H adsorption results in a removal of occupied and unoccupied intragap electron
states of the clean GaN(1-100) surface and a reduction of the surface upward
band bending by 0.4 eV. The latter mechanism largely reduces surface electron
depletion
Higher Dimensional Schwinger-like Anomalous Effective Action
We construct explicit form of the anomalous effective action, in arbitrary
even dimension, for Abelian vector and axial gauge fields coupled to Dirac
fermions. It turns out to be a surprisingly simple extension of 2D Schwinger
model effective action.Comment: 7 pages, no figures, ReVTeX, to appear in Phys.Rev.
Effective action of magnetic monopole in three-dimensional electrodynamics with massless matter and gauge theories of superconductivity
We compute one-loop effective action of magnetic monopole in
three-dimensional electrodynamics of massless bosons and fermions and find that
it contains an infrared logarithm. So, when the number of massless matter
species is sufficiently large, monopoles are suppressed and in the weak
coupling limit charged particles are unconfined. This result provides some
support to gauge theories of high-temperature superconductors. It also provides
a mechanism by which interlayer tunneling of excitations with one unit of the
ordinary electric charge can be suppressed while that of a doubly charged
object is allowed.Comment: 8 pages, LATEX, UCLA/93/TEP/41 (the last sentence of the paragraph
concerning applications at the end of the paper has been deleted; mailing
problems have been corrected
Infra-red effects of Non-linear sigma model in de Sitter space
We extend our investigation on a possible de Sitter symmetry breaking
mechanism in non-linear sigma models. The scale invariance of the quantum
fluctuations could make the cosmological constant time dependent signaling the
de Sitter symmetry breaking. To understand such a symmetry breaking mechanism,
we investigate the energy-momentum tensor. We show that the leading infra-red
logarithms cancel to all orders in perturbation theory in a generic non-linear
sigma model. When the target space is an N sphere, the de Sitter symmetry is
preserved in the large N limit. For a less symmetric target space, the
infra-red logarithms appear at the three loop level. However there is a counter
term to precisely cancel it. The leading infra-red logarithms do not cancel for
higher derivative interactions. We investigate such a model in which the
infra-red logarithms first appear at the three loop level. A nonperturbative
investigation in the large N limit shows that they eventually grow as large as
the one loop effect.Comment: 39page
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