2,260 research outputs found
Perturbative Evaluation of Interacting Scalar Fields on a Curved Manifold with Boundary
The effects of quantum corrections to a conformally invariant scalar field
theory on a curved manifold of positive constant curvature with boundary are
considered in the context of a renormalisation procedure. The renormalisation
of the theory to second order in the scalar self-coupling pursued herein
involves explicit calculations of up to third loop-order and reveals that, in
addition to the renormalisation of the scalar self-coupling and scalar field,
the removal of all divergences necessitates the introduction of conformally
non-invariant counterterms proportional to and in the
bare scalar action as well as counterterms proportional to , and
in the gravitational action. The substantial backreaction effects and
their relevance to the renormalisation procedure are analysed.Comment: 25 pages, 1 figure. Minor elucidations in the Appendix regarding the
cut-off and in p.4 regarding the gravitational action. Certain
reference-related ommission corrected. To appear in Classical and Quantum
Gravit
Spherical Formulation for Diagramatic Evaluations on a Manifold with Boundary
The mathematical formalism necessary for the diagramatic evaluation of
quantum corrections to a conformally invariant field theory for a
self-interacting scalar field on a curved manifold with boundary is considered.
The evaluation of quantum corrections to the effective action past one-loop
necessitates diagramatic techniques. Diagramatic evaluations and higher
loop-order renormalisation can be best accomplished on a Riemannian manifold of
constant curvature accommodating a boundary of constant extrinsic curvature. In
such a context the stated evaluations can be accomplished through a consistent
interpretation of the Feynman rules within the spherical formulation of the
theory for which the method of images allows. To this effect, the mathematical
consequences of such an interpretation are analyzed and the spherical
formulation of the Feynman rules on the bounded manifold is, as a result,
developed.Comment: 12 pages, references added. To appear in Classical and Quantum
Gravit
Temperature Dependence of Facet Ridges in Crystal Surfaces
The equilibrium crystal shape of a body-centered solid-on-solid (BCSOS) model
on a honeycomb lattice is studied numerically. We focus on the facet ridge
endpoints (FRE). These points are equivalent to one dimensional KPZ-type growth
in the exactly soluble square lattice BCSOS model. In our more general context
the transfer matrix is not stochastic at the FRE points, and a more complex
structure develops. We observe ridge lines sticking into the rough phase where
thesurface orientation jumps inside the rounded part of the crystal. Moreover,
the rough-to-faceted edges become first-order with a jump in surface
orientation, between the FRE point and Pokrovsky-Talapov (PT) type critical
endpoints. The latter display anisotropic scaling with exponent instead
of familiar PT value .Comment: 12 pages, 19 figure
Axial anomaly: the modern status
The modern status of the problem of axial anomaly in QED and QCD is reviewed.
Two methods of the derivation of the axial anomaly are presented: 1) by
splitting of coordinates in the expression for the axial current and 2) by
calculation of triangle diagrams, where the anomaly arises from the surface
terms in momentum space. It is demonstrated, that the equivalent formulation of
the anomaly can be given, as a sum rule for the structure function in
dispersion representation of three point function of AVV interaction. It is
argued, that such integral representation of the anomaly has some advantages in
the case of description of the anomaly by contribution of hadronic states in
QCD. The validity of the t'Hooft consistency condition is discussed. Few
examples of the physical application of the axial anomaly are given.Comment: 17 pages, 3 figures, to be published in International Journal of
Modern Physics A, few minor correction were done, two references were adde
Electromagnetic response of a static vortex line in a type-II superconductor : a microscopic study
The electromagnetic response of a pinned Abrikosov fluxoid is examined in the
framework of the Bogoliubov-de Gennes formalism. The matrix elements and the
selection rules for both the single photon (emission - absorption) and two
photon (Raman scattering) processes are obtained. The results reveal striking
asymmetries: light absorption by quasiparticle pair creation or single
quasiparticle scattering can occur only if the handedness of the incident
radiation is opposite to that of the vortex core states. We show how these
effects will lead to nonreciprocal circular birefringence, and also predict
structure in the frequency dependence of conductivity and in the differential
cross section of the Raman scattering.Comment: 14 pages (RevTex
Decoherence in ion traps due to laser intensity and phase fluctuations
We consider one source of decoherence for a single trapped ion due to
intensity and phase fluctuations in the exciting laser pulses. For simplicity
we assume that the stochastic processes involved are white noise processes,
which enables us to give a simple master equation description of this source of
decoherence. This master equation is averaged over the noise, and is sufficient
to describe the results of experiments that probe the oscillations in the
electronic populations as energy is exchanged between the internal and
electronic motion. Our results are in good qualitative agreement with recent
experiments and predict that the decoherence rate will depend on vibrational
quantum number in different ways depending on which vibrational excitation
sideband is used.Comment: 2 figures, submitted to PR
The Conical Point in the Ferroelectric Six-Vertex Model
We examine the last unexplored regime of the asymmetric six-vertex model: the
low-temperature phase of the so-called ferroelectric model. The original
publication of the exact solution, by Sutherland, Yang, and Yang, and various
derivations and reviews published afterwards, do not contain many details about
this regime. We study the exact solution for this model, by numerical and
analytical methods. In particular, we examine the behavior of the model in the
vicinity of an unusual coexistence point that we call the ``conical'' point.
This point corresponds to additional singularities in the free energy that were
not discussed in the original solution. We show analytically that in this point
many polarizations coexist, and that unusual scaling properties hold in its
vicinity.Comment: 28 pages (LaTeX); 8 postscript figures available on request
([email protected]). Submitted to Journal of Statistical Physics. SFU-DJBJDS-94-0
Generation of nonground-state Bose-Einstein condensates by modulating atomic interactions
A technique is proposed for creating nonground-state Bose-Einstein
condensates in a trapping potential by means of the temporal modulation of
atomic interactions. Applying a time-dependent spatially homogeneous magnetic
field modifies the atomic scattering length. An alternating modulation of the
scattering length excites the condensate, which, under special conditions, can
be transferred to an excited nonlinear coherent mode. It is shown that there
occurs a phase-transition-like behavior in the time-averaged population
imbalance between the ground and excited states. The application of the
suggested technique to realistic experimental conditions is analyzed and it is
shown that the considered effect can be realized for experimentally available
condensates.Comment: 6 pages, 2 figures, 1 tabl
States interpolating between number and coherent states and their interaction with atomic systems
Using the eigenvalue definition of binomial states we construct new
intermediate number-coherent states which reduce to number and coherent states
in two different limits. We reveal the connection of these intermediate states
with photon-added coherent states and investigate their non-classical
properties and quasi-probability distributions in detail. It is of interest to
note that these new states, which interpolate between coherent states and
number states, neither of which exhibit squeezing, are nevertheless squeezed
states. A scheme to produce these states is proposed. We also study the
interaction of these states with atomic systems in the framework of the
two-photon Jaynes-Cummings model, and describe the response of the atomic
system as it varies between the pure Rabi oscillation and the collapse-revival
mode and investigate field observables such as photon number distribution,
entropy and the Q-function.Comment: 26 pages, 29 EPS figures, Latex, Accepted for publication in J.Phys.
Constraints on relaxation rates for N-level quantum systems
We study the constraints imposed on the population and phase relaxation rates
by the physical requirement of completely positive evolution for open N-level
systems. The Lindblad operators that govern the evolution of the system are
expressed in terms of observable relaxation rates, explicit formulas for the
decoherence rates due to population relaxation are derived, and it is shown
that there are additional, non-trivial constraints on the pure dephasing rates
for N>2. Explicit experimentally testable inequality constraints for the
decoherence rates are derived for three and four-level systems, and the
implications of the results are discussed for generic ladder-, Lambda- and
V-systems, and transitions between degenerate energy levels.Comment: 10 pages, RevTeX, 4 figures (eps/pdf
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