520 research outputs found
Absolute continuity and spectral concentration for slowly decaying potentials
We consider the spectral function for the
Sturm-Liouville equation on with the
boundary condition and where has slow decay
as . We develop our previous methods of locating spectral
concentration for with rapid exponential decay (JCAM 81 (1997) 333-348) to
deal with the new theoretical and computational complexities which arise for
slow decay
Extensions of a New Algorithm for the Numerical Solution of Linear Differential Systems on an Infinite Interval
This paper is part of a series of papers in which the asymptotic theory and
appropriate symbolic computer code are developed to compute the asymptotic
expansion of the solution of an n-th order ordinary differential equation. The
paper examines the situation when the matrix that appears in the Levinson
expansion has a double eigenvalue. Application is made to a fourth-order ODE
with known special function solution
The new physics of non-equilibrium condensates: insights from classical dynamics
We discuss the dynamics of classical Dicke-type models, aiming to clarify the
mechanisms by which coherent states could develop in potentially
non-equilibrium systems such as semiconductor microcavities. We present
simulations of an undamped model which show spontaneous coherent states with
persistent oscillations in the magnitude of the order parameter. These states
are generalisations of superradiant ringing to the case of inhomogeneous
broadening. They correspond to the persistent gap oscillations proposed in
fermionic atomic condensates, and arise from a variety of initial conditions.
We show that introducing randomness into the couplings can suppress the
oscillations, leading to a limiting dynamics with a time-independent order
parameter. This demonstrates that non-equilibrium generalisations of polariton
condensates can be created even without dissipation. We explain the dynamical
origins of the coherence in terms of instabilities of the normal state, and
consider how it can additionally develop through scattering and dissipation.Comment: 10 pages, 4 figures, submitted for a special issue of J. Phys.:
Condensed Matter on "Optical coherence and collective phenomena in
nanostructures". v2: added discussion of links to exact solution
Mechanism for the failure of the Edwards hypothesis in the SK spin glass
The dynamics of the SK model at T=0 starting from random spin configurations
is considered. The metastable states reached by such dynamics are atypical of
such states as a whole, in that the probability density of site energies,
, is small at . Since virtually all metastable states
have a much larger , this behavior demonstrates a qualitative failure of
the Edwards hypothesis. We look for its origins by modelling the changes in the
site energies during the dynamics as a Markov process. We show how the small
arises from features of the Markov process that have a clear physical
basis in the spin-glass, and hence explain the failure of the Edwards
hypothesis.Comment: 5 pages, new title, modified text, additional reference
Massive Dirac particles on the background of charged de-Sitter black hole manifolds
We consider the behavior of massive Dirac fields on the background of a
charged de-Sitter black hole. All black hole geometries are taken into account,
including the Reissner-Nordstr\"{o}m-de-Sitter one, the Nariai case and the
ultracold case. Our focus is at first on the existence of bound quantum
mechanical states for the Dirac Hamiltonian on the given backgrounds. In this
respect, we show that in all cases no bound state is allowed, which amounts
also to the non-existence of normalizable time-periodic solutions of the Dirac
equation. This quantum result is in contrast to classical physics, and it is
shown to hold true even for extremal cases. Furthermore, we shift our attention
on the very interesting problem of the quantum discharge of the black holes.
Following Damour-Deruelle-Ruffini approach, we show that the existence of
level-crossing between positive and negative continuous energy states is a
signal of the quantum instability leading to the discharge of the black hole,
and in the cases of the Nariai geometry and of the ultracold geometries we also
calculate in WKB approximation the transmission coefficient related to the
discharge process.Comment: 19 pages, 11 figures. Macro package: Revtex4. Changes concern mainly
the introduction and the final discussion in section VI; moreover, Appendix D
on the evaluation of the Nariai transmission integral has been added.
References adde
Conditions for the spectrum associated with a leaky wire to contain the interval [− α2/4, ∞)
The method of singular sequences is used to provide a simple and, in some respects, a more general proof of a known spectral result for leaky wires. The method introduces a new concept of asymptotic straightness
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