490,979 research outputs found
Optical conductivity of unconventional charge density wave systems: Role of vertex corrections
The optical conductivity of a d-CDW conductor is calculated for electrons on
a square lattice and a nearest-neighbor charge-charge interaction using the
lowest-order conserving approximation. The spectral properties of the
Drude-like peak at low frequencies and the broad hump due to transitions across
the gap at large frequencies are discussed, also as a function of temperature
and of the second-nearest neighbor hopping term t'. We find that vertex
corrections enhance the d.c. conductivity, make the Drude peak narrower and
provide a smooth transition from a renormalized regime at low to the bare
theory at high frequencies. It is also shown that vertex corrections enhance
the temperature dependence of the restricted optical sum leading to a
non-negligible violation of the sum rule in the d-CDW state.Comment: 10 pages, 6 figure
Classification of five-point differential-difference equations
Using the generalized symmetry method, we carry out, up to autonomous point
transformations, the classification of integrable equations of a subclass of
the autonomous five-point differential-difference equations. This subclass
includes such well-known examples as the Itoh-Narita-Bogoyavlensky and the
discrete Sawada-Kotera equations. The resulting list contains 17 equations some
of which seem to be new. We have found non-point transformations relating most
of the resulting equations among themselves and their generalized symmetries.Comment: 29 page
Approaches to Three-Dimensional Transformation Optical Media Using Quasi-Conformal Coordinate Transformations
We introduce an approach to the design of three-dimensional transformation
optical (TO) media based on a generalized quasi-conformal mapping approach. The
generalized quasi-conformal TO (QCTO) approach enables the design of media that
can, in principle, be broadband and low-loss, while controlling the propagation
of waves with arbitrary angles of incidence and polarization. We illustrate the
method in the design of a three-dimensional "carpet" ground plane cloak and of
a flattened Luneburg lens. Ray-trace studies provide a confirmation of the
performance of the QCTO media, while also revealing the limited performance of
index-only versions of these devices
Covariance, correlation and entanglement
Some new identities for quantum variance and covariance involving commutators
are presented, in which the density matrix and the operators are treated
symmetrically. A measure of entanglement is proposed for bipartite systems,
based on covariance. This works for two- and three-component systems but
produces ambiguities for multicomponent systems of composite dimension. Its
relationship to angular momentum dispersion for symmetric symmetric spin states
is described.Comment: 30 pages, Latex, to appear in J Phys
Asymptotic properties of mathematical models of excitability
We analyse small parameters in selected models of biological excitability,
including Hodgkin-Huxley (1952) model of nerve axon, Noble (1962) model of
heart Purkinje fibres, and Courtemanche et al. (1998) model of human atrial
cells. Some of the small parameters are responsible for differences in the
characteristic timescales of dynamic variables, as in the traditional singular
perturbation approaches. Others appear in a way which makes the standard
approaches inapplicable. We apply this analysis to study the behaviour of
fronts of excitation waves in spatially-extended cardiac models. Suppressing
the excitability of the tissue leads to a decrease in the propagation speed,
but only to a certain limit; further suppression blocks active propagation and
leads to a passive diffusive spread of voltage. Such a dissipation may happen
if a front propagates into a tissue recovering after a previous wave, e.g.
re-entry. A dissipated front does not recover even when the excitability
restores. This has no analogy in FitzHugh-Nagumo model and its variants, where
fronts can stop and then start again. In two spatial dimensions, dissipation
accounts for break-ups and self-termination of re-entrant waves in excitable
media with Courtemanche et al. (1998) kinetics.Comment: 15 pages, 8 figures, to appear in Phil Trans Roy Soc London
Large rare fluctuations in systems with delayed dissipation
We study the probability distribution and the escape rate in systems with
delayed dissipation that comes from the coupling to a thermal bath. To
logarithmic accuracy in the fluctuation intensity, the problem is reduced to a
variational problem. It describes the most probable fluctuational paths, which
are given by acausal equations due to the delay. In thermal equilibrium, the
most probable path passing through a remote state has time reversal symmetry,
even though one cannot uniquely define a path that starts from a state with
given system coordinate and momentum. The corrections to the distribution and
the escape activation energy for small delay and small noise correlation time
are obtained in the explicit form.Comment: 9 page
NICMOS and VLBA observations of the gravitational lens system B1933+503
NICMOS observations of the complex gravitational lens system B1933+503 reveal
infrared counterparts to two of the inverted spectrum radio images. The
infrared images have arc-like structures. The corresponding radio images are
also detected in a VLBA map made at 1.7 GHz with a resolution of 6 mas. We fail
to detect two of the four inverted radio spectrum components with the VLBA even
though they are clearly visible in a MERLIN map at the same frequency at a
different epoch. The absence of these two components could be due to rapid
variability on a time-scale less than the time delay, or to broadening of the
images during propagation of the radio waves through the ISM of the lensing
galaxy to an extent that they fall below the surface brightness detectability
threshold of the VLBA observations. The failure to detect the same two images
with NICMOS is probably due to extinction in the ISM of the lensing galaxy.Comment: 5 pages, 4 figures, submitted to MNRA
- …