17,939 research outputs found
From K.A.M. Tori to Isospectral Invariants and Spectral Rigidity of Billiard Tables
This article is a part of a project investigating the relationship between
the dynamics of completely integrable or close to completely integrable
billiard tables, the integral geometry on them, and the spectrum of the
corresponding Laplace-Beltrami operators. It is concerned with new isospectral
invariants and with the spectral rigidity problem for families of
Laplace-Beltrami operators with Dirichlet, Neumann or Robin boundary
conditions, associated with C^1 families of billiard tables. We introduce a
notion of weak isospectrality for such deformations. The main dynamical
assumption on the initial billiard table is that the corresponding billiard
ball map or an iterate of it has a Kronecker invariant torus with a Diophantine
frequency and that the corresponding Birkhoff Normal Form is nondegenerate in
Kolmogorov sense. Then we obtain C^1 families of Kronecker tori with
Diophantine frequencies. If the family of the Laplace-Beltrami operators
satisfies the weak isospectral condition, we prove that the average action on
the tori and the Birkhoff Normal Form of the billiard ball maps remain the same
along the perturbation. As an application we obtain infinitesimal spectral
rigidity for Liouville billiard tables in dimensions two and three.
Applications are obtained also for strictly convex billiard tables of dimension
two as well as in the case when the initial billiard table admits an elliptic
periodic billiard trajectory. Spectral rigidity of billard tables close
elliptical billiard tables is obtained. The results are based on a construction
of C^1 families of quasi-modes associated with the Kronecker tori and on
suitable KAM theorems for C^1 families of Hamiltonians.Comment: 170 pages; new results about the spectral rigidity of elliptical
billiard tables; new Modified Iterative Lemma in the proof of KAM theorem
with parameter
Atomic coherence and interference phenomena in resonant nonlinear optical interactions
Interference effects in quantum transitions, giving rise to amplification
without inversion, optical transparency and to enhancements in nonlinear
optical frequency conversions are considered. Review of the relevant early
theoretical and experimental results is given. The role of relaxation
processes, spontaneous cascade of polarizations, local field effects,
Doppler-broadening, as well as specific features of the interference in the
spectral continuum are discussed.Comment: 13 pages, 13 eps figures, review paper, Proceedings of the 15th
International Conference on Nonlinear Optics - ICONO'9
Asymmetric tunneling, Andreev reflection and dynamic conductance spectra in strongly correlated metals
Landau Fermi liquid theory predicts that the differential conductivity
between metallic point and metal is a symmetric function of voltage bias V.
This symmetry holds if the particle-hole symmetry is preserved. We show that
the situation can be different when one of the two metals is a strongly
correlated one whose electronic system can be represented by a heavy fermion
liquid. When the heavy fermion liquid undergoes fermion condensation quantum
phase transition, the particle-hole symmetry is violated making both the
differential tunneling conductivity and dynamic conductance asymmetric as a
function of applied voltage. This asymmetry can be observed when the strongly
correlated metal is either normal or superconducting. We show that at small
values of $V the asymmetric part of the dynamic conductance is a linear
function of V and inversely proportional to the maximum value of the gap and
does not depend on temperature provided that metal is superconducting, when it
becomes normal the asymmetric part diminishes at elevated temperatures.Comment: 8 pages, 7 figure
Finite linear groups, lattices, and products of elliptic curves
Let be a finite dimensional complex linear space and let be an
irreducible finite subgroup of \GL(V). For a -invariant lattice
in of maximal rank, we give a description of structure of the complex torus
. In particular, we prove that for a wide class of groups,
is isogenous to a self-product of an elliptic curve, and that in
many cases is isomorphic to a product of mutually isogenous
elliptic curves with complex multiplication. We show that there are and
such that the complex torus is not an abelian variety but
one can always replace by another -invariant lattice such
that is a product if elliptic curves with complex multiplication. We
amplify these results with a criterion, in terms of the character and the Schur
-index of -module , of the existence of a nonzero
-invariant lattice in .Comment: 25 pages. Several examples are adde
Enhanced four-wave mixing via elimination of inhomogeneous broadening by coherent driving of quantum transition with control fields
We show that atoms from wide velocity interval can be concurrently involved
in Doppler-free two-photon resonant far from frequency degenerate four-wave
mixing with the aid of auxiliary electromagnetic field. This gives rise to
substantial enhancement of the output radiation generated in optically thick
medium. Numerical illustrations addressed to typical experimental conditions
are given.Comment: LaTeX2e, hyperref, 7 pages, 5 figures, to appear in PRA 1 august 200
The experimental study of the surface current excitation under the influence of a relativistic electron electromagnetic field
The problem of the surface current excitation in a conductive targets by a
relativistic electron electric field as the origin of such radiation mechanisms
as diffraction and transition radiation of relativistic electron was considered
in frame of both surface current and pseudo-photon methods. The contradiction
between these viewpoints in respect to the surface current on the target
downstream surface necessitated the experimental test of this phenomenon. The
test performed on electron beam of the 6 MeV microtron showed, that not any
surface current is induced on the target downstream surface under the influence
of a relativistic electron electromagnetic field in contrast to the upstream
surface. This is important implication for the understanding of the forward
transition and diffraction radiation nature.Comment: Was Presented at the symposium Channeling 2008 (Charged and Neutral
Particles Channeling Phenomena), October 25 - November 1, 2008 Erice (Trapani
- Sicily), Italy, and was accepted for publication in proceedings of
symposiu
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