886 research outputs found
On Hirschman and log-Sobolev inequalities in mu-deformed Segal-Bargmann analysis
We consider a deformation of Segal-Bargmann space and its transform. We study
L^p properties of this transform and obtain entropy-entropy inequalities
(Hirschman) and entropy-energy inequalities (log-Sobolev) that generalize the
corresponding known results in the undeformed theory.Comment: 42 pages, 3 figure
Self-adjoint Lyapunov variables, temporal ordering and irreversible representations of Schroedinger evolution
In non relativistic quantum mechanics time enters as a parameter in the
Schroedinger equation. However, there are various situations where the need
arises to view time as a dynamical variable. In this paper we consider the
dynamical role of time through the construction of a Lyapunov variable - i.e.,
a self-adjoint quantum observable whose expectation value varies monotonically
as time increases. It is shown, in a constructive way, that a certain class of
models admit a Lyapunov variable and that the existence of a Lyapunov variable
implies the existence of a transformation mapping the original quantum
mechanical problem to an equivalent irreversible representation. In addition,
it is proved that in the irreversible representation there exists a natural
time ordering observable splitting the Hilbert space at each t>0 into past and
future subspaces.Comment: Accepted for publication in JMP. Supercedes arXiv:0710.3604.
Discussion expanded to include the case of Hamiltonians with an infinitely
degenerate spectru
Matricial Baxter's theorem with a Nehari sequence
In the theory of orthogonal polynomials, (non‐trivial) probability measures on the unit circle are parametrized by the Verblunsky coefficients. Baxter's theorem asserts that such a measure is absolutely continuous and has positive density with summable Fourier coefficients if and only if its Verblusnky coefficients are summable. This note presents a version of Baxter's theorem in the matrix case from a viewpoint of the Nehari problem
Conspicuous male coloration impairs survival against avian predators in Aegean wall lizards, Podarcis erhardii.
This is the final version of the article. It first appeared from Wiley via http://dx.doi.org/10.1002/ece3.1650Animal coloration is strikingly diverse in nature. Within-species color variation can arise through local adaptation for camouflage, sexual dimorphism and conspicuous sexual signals, which often have conflicting effects on survival. Here, we tested whether color variation between two island populations of Aegean wall lizards (Podarcis erhardii) is due to sexual dimorphism and differential survival of individuals varying in appearance. On both islands, we measured attack rates by wild avian predators on clay models matching the coloration of real male and female P. erhardii from each island population, modeled to avian predator vision. Avian predator attack rates differed among model treatments, although only on one island. Male-colored models, which were more conspicuous against their experimental backgrounds to avian predators, were accordingly detected and attacked more frequently by birds than less conspicuous female-colored models. This suggests that female coloration has evolved primarily under selection for camouflage, whereas sexually competing males exhibit costly conspicuous coloration. Unexpectedly, there was no difference in avian attack frequency between local and non-local model types. This may have arisen if the models did not resemble lizard coloration with sufficient precision, or if real lizards behaviorally choose backgrounds that improve camouflage. Overall, these results show that sexually dimorphic coloration can affect the risk of predator attacks, indicating that color variation within a species can be caused by interactions between natural and sexual selection. However, more work is needed to determine how these findings depend on the island environment that each population inhabits.This work was supported by a Biotechnology and Biological Sciences Research Council studentship, Magdalene College, Cambridge and the British Herpetological Society (K.L.A.M), and a Biotechnology and Biological Sciences Research Council and David Philips Research Fellowship (grant number BB/G022887/1) to M.S
Synchronization of chaotic oscillator time scales
This paper deals with the chaotic oscillator synchronization. A new approach
to detect the synchronized behaviour of chaotic oscillators has been proposed.
This approach is based on the analysis of different time scales in the time
series generated by the coupled chaotic oscillators. It has been shown that
complete synchronization, phase synchronization, lag synchronization and
generalized synchronization are the particular cases of the synchronized
behavior called as "time--scale synchronization". The quantitative measure of
chaotic oscillator synchronous behavior has been proposed. This approach has
been applied for the coupled Rossler systems.Comment: 29 pages, 11 figures, published in JETP. 100, 4 (2005) 784-79
Inverse Spectral-Scattering Problem with Two Sets of Discrete Spectra for the Radial Schroedinger Equation
The Schroedinger equation on the half line is considered with a real-valued,
integrable potential having a finite first moment. It is shown that the
potential and the boundary conditions are uniquely determined by the data
containing the discrete eigenvalues for a boundary condition at the origin, the
continuous part of the spectral measure for that boundary condition, and a
subset of the discrete eigenvalues for a different boundary condition. This
result extends the celebrated two-spectrum uniqueness theorem of Borg and
Marchenko to the case where there is also a continuous spectru
Recognising facial expressions in video sequences
We introduce a system that processes a sequence of images of a front-facing human face and recognises a set of facial expressions. We use an efficient appearance-based face tracker to locate the face in the image sequence and estimate the deformation of its non-rigid components. The tracker works in real-time. It is robust to strong illumination changes and factors out changes in appearance caused by illumination from changes due to face deformation. We adopt a model-based approach for facial expression recognition. In our model, an image of a face is represented by a point in a deformation space. The variability of the classes of images associated to facial expressions are represented by a set of samples which model a low-dimensional manifold in the space of deformations. We introduce a probabilistic procedure based on a nearest-neighbour approach to combine the information provided by the incoming image sequence with the prior information stored in the expression manifold in order to compute a posterior probability associated to a facial expression. In the experiments conducted we show that this system is able to work in an unconstrained environment with strong changes in illumination and face location. It achieves an 89\% recognition rate in a set of 333 sequences from the Cohn-Kanade data base
Resonant two-magnon Raman scattering in parent compounds of high-T superconductors.
We propose a theory of two-magnon Raman scattering from the insulating parent
compounds of high-T superconductors, which contains information not only on
magnetism, but also on the electronic properties in these materials. We use
spin density wave formalism for the Hubbard model, and study diagrammatically
the profile of the two-magnon scattering and its intensity dependence on the
incoming photon frequency both for and in the
resonant regime, in which the energy of the incident photon is close to the gap
between conduction and valence bands. In the nonresonant case, we identify the
diagrams which contribute to the conventional Loudon-Fleury Hamiltonian. In the
resonant regime, where most of the experiments have been done, we find that the
dominant contribution to Raman intensity comes from a different diagram, one
which allows for a simultaneous vanishing of all three of its denominators
(i.e., a triple resonance). We study this diagram in detail and show that the
triple resonance, combined with the spin-density-wave dispersion relation for
the carriers, explains the unusual features found in the two-magnon profile and
in the two-magnon peak intensity dependence on the incoming photon frequency.
In particular, our theory predicts a maximum of the two-magnon peak intensity
right at the upper edge of the features in the optical data, which has been one
of the key experimental puzzles.Comment: Revtex, 12 postscript figures (uuencoded
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