398 research outputs found
Conical diffraction and the dispersion surface of hyperbolic metamaterials
Hyperbolic metamaterials are materials in which at least one principal
dielectric constant is negative. We describe the refractive index surface, and
the resulting refraction effects, for a biaxial hyperbolic metamaterial, with
principal dielectric constants , . In
this general case the two sheets of the index surface intersect forming conical
singularities. We derive the ray description of conical refraction in these
materials, and show that it is topologically and quantitatively distinct from
conical refraction in a conventional biaxial material. We also develop a wave
optics description, which allows us to obtain the diffraction patterns formed
from arbitrary beams incident close to the optic axis. The resulting patterns
lack circular symmetry, and hence are qualitatively different from those
obtained in conventional, positive index materials.Comment: 10 pages, 7 figure
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
Quantum properties of the Dirac field on BTZ black hole backgrounds
We consider a Dirac field on a -dimensional uncharged BTZ black hole
background. We first find out the Dirac Hamiltonian, and study its
self-adjointness properties. We find that, in analogy to the Kerr-Newman-AdS
Dirac Hamiltonian in dimensions, essential self-adjointness on
of the reduced (radial) Hamiltonian is implemented
only if a suitable relation between the mass of the Dirac field and the
cosmological radius holds true. The very presence of a boundary-like
behaviour of is at the root of this problem. Also, we determine in a
complete way qualitative spectral properties for the non-extremal case, for
which we can infer the absence of quantum bound states for the Dirac field.
Next, we investigate the possibility of a quantum loss of angular momentum for
the -dimensional uncharged BTZ black hole. Unlike the corresponding
stationary four-dimensional solutions, the formal treatment of the level
crossing mechanism is much simpler. We find that, even in the extremal case, no
level crossing takes place. Therefore, no quantum loss of angular momentum via
particle pair production is allowed.Comment: 19 pages; IOP styl
Absence of Normalizable Time-periodic Solutions for The Dirac Equation in Kerr-Newman-dS Black Hole Background
We consider the Dirac equation on the background of a Kerr-Newman-de Sitter
black hole. By performing variable separation, we show that there exists no
time-periodic and normalizable solution of the Dirac equation. This conclusion
holds true even in the extremal case. With respect to previously considered
cases, the novelty is represented by the presence, together with a black hole
event horizon, of a cosmological (non degenerate) event horizon, which is at
the root of the possibility to draw a conclusion on the aforementioned topic in
a straightforward way even in the extremal case.Comment: 12 pages. AMS styl
BCS-BEC crossover in a system of microcavity polaritons
We investigate the thermodynamics and signatures of a polariton condensate
over a range of densities, using a model of microcavity polaritons with
internal structure. We determine a phase diagram for this system including
fluctuation corrections to the mean-field theory. At low densities the
condensation temperature, T_c, behaves like that for point bosons. At higher
densities, when T_c approaches the Rabi splitting, T_c deviates from the form
for point bosons, and instead approaches the result of a BCS-like mean-field
theory. This crossover occurs at densities much less than the Mott density. We
show that current experiments are in a density range where the phase boundary
is described by the BCS-like mean-field boundary. We investigate the influence
of inhomogeneous broadening and detuning of excitons on the phase diagram.Comment: 20 pages, 6 figure
Relative Oscillation Theory, Weighted Zeros of the Wronskian, and the Spectral Shift Function
We develop an analog of classical oscillation theory for Sturm-Liouville
operators which, rather than measuring the spectrum of one single operator,
measures the difference between the spectra of two different operators.
This is done by replacing zeros of solutions of one operator by weighted
zeros of Wronskians of solutions of two different operators. In particular, we
show that a Sturm-type comparison theorem still holds in this situation and
demonstrate how this can be used to investigate the finiteness of eigenvalues
in essential spectral gaps. Furthermore, the connection with Krein's spectral
shift function is established.Comment: 26 page
Polariton condensation and lasing in optical microcavities - the decoherence driven crossover
We explore the behaviour of a system which consists of a photon mode dipole
coupled to a medium of two-level oscillators in a microcavity in the presence
of decoherence. We consider two types of decoherence processes which are
analogous to magnetic and non-magnetic impurities in superconductors. We study
different phases of this system as the decoherence strength and the excitation
density is changed. For a low decoherence we obtain a polariton condensate with
comparable excitonic and photonic parts at low densities and a BCS-like state
with bigger photon component due to the fermionic phase space filling effect at
high densities. In both cases there is a large gap in the density of states. As
the decoherence is increased the gap is broadened and suppressed, resulting in
a gapless condensate and finally a suppression of the coherence in a low
density regime and a laser at high density limit. A crossover between these
regimes is studied in a self-consistent way analogous to the Abrikosov and
Gor'kov theory of gapless superconductivity.Comment: 17 pages, 8 figures, submitted to PR
The Central Singularity in Spherical Collapse
The gravitational strength of the central singularity in spherically
symmetric space-times is investigated. Necessary conditions for the singularity
to be gravitationally weak are derived and it is shown that these are violated
in a wide variety of circumstances. These conditions allow conclusions to be
drawn about the nature of the singularity without having to integrate the
geodesic equations. In particular, any geodesic with a non-zero amount of
angular momentum which impinges on the singularity terminates in a strong
curvature singularity.Comment: 17 pages; revised and corrected with improved result
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