487 research outputs found
Nonuniversality in level dynamics
Statistical properties of parametric motion in ensembles of Hermitian banded
random matrices are studied. We analyze the distribution of level velocities
and level curvatures as well as their correlation functions in the crossover
regime between three universality classes. It is shown that the statistical
properties of level dynamics are in general non-universal and strongly depend
on the way in which the parametric dynamics is introduced.Comment: 24 pages + 10 figures (not included, avaliable from the author),
submitted to Phys. Rev.
Spontaneous emission of non-dispersive Rydberg wave packets
Non dispersive electronic Rydberg wave packets may be created in atoms
illuminated by a microwave field of circular polarization. We discuss the
spontaneous emission from such states and show that the elastic incoherent
component (occuring at the frequency of the driving field) dominates the
spectrum in the semiclassical limit, contrary to earlier predictions. We
calculate the frequencies of single photon emissions and the associated rates
in the "harmonic approximation", i.e. when the wave packet has approximately a
Gaussian shape. The results agree well with exact quantum mechanical
calculations, which validates the analytical approach.Comment: 14 pages, 4 figure
Symplectic Microgeometry II: Generating functions
We adapt the notion of generating functions for lagrangian submanifolds to
symplectic microgeometry. We show that a symplectic micromorphism always admits
a global generating function. As an application, we describe hamiltonian flows
as special symplectic micromorphisms whose local generating functions are the
solutions of Hamilton-Jacobi equations. We obtain a purely categorical
formulation of the temporal evolution in classical mechanics.Comment: 27 pages, 1 figur
Surfaces immersed in su(N+1) Lie algebras obtained from the CP^N sigma models
We study some geometrical aspects of two dimensional orientable surfaces
arrising from the study of CP^N sigma models. To this aim we employ an
identification of R^(N(N+2)) with the Lie algebra su(N+1) by means of which we
construct a generalized Weierstrass formula for immersion of such surfaces. The
structural elements of the surface like its moving frame, the Gauss-Weingarten
and the Gauss-Codazzi-Ricci equations are expressed in terms of the solution of
the CP^N model defining it. Further, the first and second fundamental forms,
the Gaussian curvature, the mean curvature vector, the Willmore functional and
the topological charge of surfaces are expressed in terms of this solution. We
present detailed implementation of these results for surfaces immersed in su(2)
and su(3) Lie algebras.Comment: 32 pages, 1 figure; changes: major revision of presentation,
clarifications adde
Ionization via Chaos Assisted Tunneling
A simple example of quantum transport in a classically chaotic system is
studied. It consists in a single state lying on a regular island (a stable
primary resonance island) which may tunnel into a chaotic sea and further
escape to infinity via chaotic diffusion. The specific system is realistic : it
is the hydrogen atom exposed to either linearly or circularly polarized
microwaves. We show that the combination of tunneling followed by chaotic
diffusion leads to peculiar statistical fluctuation properties of the energy
and the ionization rate, especially to enhanced fluctuations compared to the
purely chaotic case. An appropriate random matrix model, whose predictions are
analytically derived, describes accurately these statistical properties.Comment: 30 pages, 11 figures, RevTeX and postscript, Physical Review E in
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Changes in Floquet state structure at avoided crossings: delocalization and harmonic generation
Avoided crossings are common in the quasienergy spectra of strongly driven
nonlinear quantum wells. In this paper we examine the sinusoidally driven
particle in a square potential well to show that avoided crossings can alter
the structure of Floquet states in this system. Two types of avoided crossings
are identified: on type leads only to temporary changes (as a function of
driving field strength) in Floquet state structure while the second type can
lead to permanent delocalization of the Floquet states. Radiation spectra from
these latter states show significant increase in high harmonic generation as
the system passes through the avoided crossing.Comment: 8 pages with 10 figures submitted to Physical Review
Squeezing of electromagnetic field in a cavity by electrons in Trojan states
The notion of the Trojan state of a Rydberg electron, introduced by
I.Bialynicki-Birula, M.Kali\'nski, and J.H.Eberly (Phys. Rev. Lett. 73, 1777
(1994)) is extended to the case of the electromagnetic field quantized in
acavity. The shape of the electronic wave packet describing the Trojan state is
practically the same as in the previously studied externally driven system. The
fluctuations of the quantized electromagnetic field around its classical value
exhibit strong squeezing. The emergence of Trojan states in the cylindrically
symmetrical system is attributed to spontaneous symmetry braking.Comment: 9 pages, 8 figure
New time-type and space-type non-standard quantum algebras and discrete symmetries
Starting from the classical r-matrix of the non-standard (or Jordanian)
quantum deformation of the sl(2,R) algebra, new triangular quantum deformations
for the real Lie algebras so(2,2), so(3,1) and iso(2,1) are simultaneously
constructed by using a graded contraction scheme; these are realized as
deformations of conformal algebras of (1+1)-dimensional spacetimes. Time-type
and space-type quantum algebras are considered according to the generator that
remains primitive after deformation: either the time or the space translation,
respectively. Furthermore by introducing differential-difference conformal
realizations, these families of quantum algebras are shown to be the symmetry
algebras of either a time or a space discretization of (1+1)-dimensional (wave
and Laplace) equations on uniform lattices; the relationship with the known Lie
symmetry approach to these discrete equations is established by means of twist
maps.Comment: 17 pages, LaTe
Polarization instabilities in a two-photon laser
We describe the operating characteristics of a new type of quantum oscillator
that is based on a two-photon stimulated emission process. This two-photon
laser consists of spin-polarized and laser-driven K atoms placed in a
high-finesse transverse-mode-degenerate optical resonator, and produces a beam
with a power of 0.2 W at a wavelength of 770 nm. We observe
complex dynamical instabilities of the state of polarization of the two-photon
laser, which are made possible by the atomic Zeeman degeneracy. We conjecture
that the laser could emit polarization-entangled twin beams if this degeneracy
is lifted.Comment: Accepted by Physical Review Letters. REVTeX 4 pages, 4 EPS figure
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