5,416 research outputs found
Band Distributions for Quantum Chaos on the Torus
Band distributions (BDs) are introduced describing quantization in a toral
phase space. A BD is the uniform average of an eigenstate phase-space
probability distribution over a band of toral boundary conditions. A general
explicit expression for the Wigner BD is obtained. It is shown that the Wigner
functions for {\em all} of the band eigenstates can be reproduced from the
Wigner BD. Also, BDs are shown to be closer to classical distributions than
eigenstate distributions. Generalized BDs, associated with sets of adjacent
bands, are used to extend in a natural way the Chern-index characterization of
the classical-quantum correspondence on the torus to arbitrary rational values
of the scaled Planck constant.Comment: 12 REVTEX page
Topological properties of quantum periodic Hamiltonians
We consider periodic quantum Hamiltonians on the torus phase space
(Harper-like Hamiltonians). We calculate the topological Chern index which
characterizes each spectral band in the generic case. This calculation is made
by a semi-classical approach with use of quasi-modes. As a result, the Chern
index is equal to the homotopy of the path of these quasi-modes on phase space
as the Floquet parameter (\theta) of the band is varied. It is quite
interesting that the Chern indices, defined as topological quantum numbers, can
be expressed from simple properties of the classical trajectories.Comment: 27 pages, 14 figure
Adiabatically coupled systems and fractional monodromy
We present a 1-parameter family of systems with fractional monodromy and
adiabatic separation of motion. We relate the presence of monodromy to a
redistribution of states both in the quantum and semi-quantum spectrum. We show
how the fractional monodromy arises from the non diagonal action of the
dynamical symmetry of the system and manifests itself as a generic property of
an important subclass of adiabatically coupled systems
On semiclassical dispersion relations of Harper-like operators
We describe some semiclassical spectral properties of Harper-like operators,
i.e. of one-dimensional quantum Hamiltonians periodic in both momentum and
position. The spectral region corresponding to the separatrices of the
classical Hamiltonian is studied for the case of integer flux. We derive
asymptotic formula for the dispersion relations, the width of bands and gaps,
and show how geometric characteristics and the absence of symmetries of the
Hamiltonian influence the form of the energy bands.Comment: 13 pages, 8 figures; final version, to appear in J. Phys. A (2004
Low voltage supply system for the very front end readout electronics of the CMS electromagnetic calorimeter
Radial velocity eclipse mapping of exoplanets
Planetary rotation rates and obliquities provide information regarding the
history of planet formation, but have not yet been measured for evolved
extrasolar planets. Here we investigate the theoretical and observational
perspective of the Rossiter-McLauglin effect during secondary eclipse (RMse)
ingress and egress for transiting exoplanets. Near secondary eclipse, when the
planet passes behind the parent star, the star sequentially obscures light from
the approaching and receding parts of the rotating planetary surface. The
temporal block of light emerging from the approaching (blue-shifted) or
receding (red-shifted) parts of the planet causes a temporal distortion in the
planet's spectral line profiles resulting in an anomaly in the planet's radial
velocity curve. We demonstrate that the shape and the ratio of the
ingress-to-egress radial velocity amplitudes depends on the planetary
rotational rate, axial tilt and impact factor (i.e. sky-projected planet
spin-orbital alignment). In addition, line asymmetries originating from
different layers in the atmosphere of the planet could provide information
regarding zonal atmospheric winds and constraints on the hot spot shape for
giant irradiated exoplanets. The effect is expected to be most-pronounced at
near-infrared wavelengths, where the planet-to-star contrasts are large. We
create synthetic near-infrared, high-dispersion spectroscopic data and
demonstrate how the sky-projected spin axis orientation and equatorial velocity
of the planet can be estimated. We conclude that the RMse effect could be a
powerful method to measure exoplanet spins.Comment: 7 pages, 3 figures, 1 table, accepted for publication in ApJ on 2015
June 1
Antiresonance and Localization in Quantum Dynamics
The phenomenon of quantum antiresonance (QAR), i.e., exactly periodic
recurrences in quantum dynamics, is studied in a large class of nonintegrable
systems, the modulated kicked rotors (MKRs). It is shown that asymptotic
exponential localization generally occurs for (a scaled ) in the
infinitesimal vicinity of QAR points . The localization length
is determined from the analytical properties of the kicking potential. This
``QAR-localization" is associated in some cases with an integrable limit of the
corresponding classical systems. The MKR dynamical problem is mapped into
pseudorandom tight-binding models, exhibiting dynamical localization (DL). By
considering exactly-solvable cases, numerical evidence is given that
QAR-localization is an excellent approximation to DL sufficiently close to QAR.
The transition from QAR-localization to DL in a semiclassical regime, as
is varied, is studied. It is shown that this transition takes place via a
gradual reduction of the influence of the analyticity of the potential on the
analyticity of the eigenstates, as the level of chaos is increased.Comment: To appear in Physical Review E. 51 pre-print pages + 9 postscript
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