476 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
Diamagnetism and flux creep in bilayer exciton superfluids
We discuss the diamagnetism induced in an isolated quantum Hall bilayer with
total filling factor one by an in-plane magnetic field. This is a signature of
counterflow superfluidity in these systems. We calculate magnetically induced
currents in the presence of pinned vortices nucleated by charge disorder, and
predict a history-dependent diamagnetism that could persist on laboratory
timescales. For current samples we find that the maximum in-plane moment is
small, but with stronger tunneling the moments would be measurable using torque
magnetometry. Such experiments would allow the persistent currents of a
counterflow superfluid to be observed in an electrically isolated bilayer.Comment: 8 pages, 2 figures. v2: updated to accepted version, extended
presentatio
Justification of the coupled-mode approximation for a nonlinear elliptic problem with a periodic potential
Coupled-mode systems are used in physical literature to simplify the
nonlinear Maxwell and Gross-Pitaevskii equations with a small periodic
potential and to approximate localized solutions called gap solitons by
analytical expressions involving hyperbolic functions. We justify the use of
the one-dimensional stationary coupled-mode system for a relevant elliptic
problem by employing the method of Lyapunov--Schmidt reductions in Fourier
space. In particular, existence of periodic/anti-periodic and decaying
solutions is proved and the error terms are controlled in suitable norms. The
use of multi-dimensional stationary coupled-mode systems is justified for
analysis of bifurcations of periodic/anti-periodic solutions in a small
multi-dimensional periodic potential.Comment: 18 pages, no figure
Far-off-resonant wave interaction in one-dimensional photonic crystals with quadratic nonlinearity
We extend a recently developed Hamiltonian formalism for nonlinear wave
interaction processes in spatially periodic dielectric structures to the
far-off-resonant regime, and investigate numerically the three-wave resonance
conditions in a one-dimensional optical medium with nonlinearity.
In particular, we demonstrate that the cascading of nonresonant wave
interaction processes generates an effective nonlinear response in
these systems. We obtain the corresponding coupling coefficients through
appropriate normal form transformations that formally lead to the Zakharov
equation for spatially periodic optical media.Comment: 14 pages, 4 figure
Photonic Band Gaps of Three-Dimensional Face-Centered Cubic Lattices
We show that the photonic analogue of the Korringa-Kohn-Rostocker method is a
viable alternative to the plane-wave method to analyze the spectrum of
electromagnetic waves in a three-dimensional periodic dielectric lattice.
Firstly, in the case of an fcc lattice of homogeneous dielectric spheres, we
reproduce the main features of the spectrum obtained by the plane wave method,
namely that for a sufficiently high dielectric contrast a full gap opens in the
spectrum between the eights and ninth bands if the dielectric constant
of spheres is lower than the dielectric constant of
the background medium. If , no gap is found in the
spectrum. The maximal value of the relative band-gap width approaches 14% in
the close-packed case and decreases monotonically as the filling fraction
decreases. The lowest dielectric contrast for which a
full gap opens in the spectrum is determined to be 8.13. Eventually, in the
case of an fcc lattice of coated spheres, we demonstrate that a suitable
coating can enhance gap widths by as much as 50%.Comment: 19 pages, 6 figs., plain latex - a section on coated spheres, two
figures, and a few references adde
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
- …