521 research outputs found
Poincar\'e Husimi representation of eigenstates in quantum billiards
For the representation of eigenstates on a Poincar\'e section at the boundary
of a billiard different variants have been proposed. We compare these
Poincar\'e Husimi functions, discuss their properties and based on this select
one particularly suited definition. For the mean behaviour of these Poincar\'e
Husimi functions an asymptotic expression is derived, including a uniform
approximation. We establish the relation between the Poincar\'e Husimi
functions and the Husimi function in phase space from which a direct physical
interpretation follows. Using this, a quantum ergodicity theorem for the
Poincar\'e Husimi functions in the case of ergodic systems is shown.Comment: 17 pages, 5 figures. Figs. 1,2,5 are included in low resolution only.
For a version with better resolution see
http://www.physik.tu-dresden.de/~baecker
About ergodicity in the family of limacon billiards
By continuation from the hyperbolic limit of the cardioid billiard we show
that there is an abundance of bifurcations in the family of limacon billiards.
The statistics of these bifurcation shows that the size of the stable intervals
decreases with approximately the same rate as their number increases with the
period. In particular, we give numerical evidence that arbitrarily close to the
cardioid there are elliptic islands due to orbits created in saddle node
bifurcations. This shows explicitly that if in this one parameter family of
maps ergodicity occurs for more than one parameter the set of these parameter
values has a complicated structure.Comment: 17 pages, 9 figure
Chaotic eigenfunctions in momentum space
We study eigenstates of chaotic billiards in the momentum representation and
propose the radially integrated momentum distribution as useful measure to
detect localization effects. For the momentum distribution, the radially
integrated momentum distribution, and the angular integrated momentum
distribution explicit formulae in terms of the normal derivative along the
billiard boundary are derived. We present a detailed numerical study for the
stadium and the cardioid billiard, which shows in several cases that the
radially integrated momentum distribution is a good indicator of localized
eigenstates, such as scars, or bouncing ball modes. We also find examples,
where the localization is more strongly pronounced in position space than in
momentum space, which we discuss in detail. Finally applications and
generalizations are discussed.Comment: 30 pages. The figures are included in low resolution only. For a
version with figures in high resolution see
http://www.physik.uni-ulm.de/theo/qc/ulm-tp/tp99-2.htm
Fractional-Power-Law Level-Statistics due to Dynamical Tunneling
For systems with a mixed phase space we demonstrate that dynamical tunneling
universally leads to a fractional power law of the level-spacing distribution
P(s) over a wide range of small spacings s. Going beyond Berry-Robnik
statistics, we take into account that dynamical tunneling rates between the
regular and the chaotic region vary over many orders of magnitude. This results
in a prediction of P(s) which excellently describes the spectral data of the
standard map. Moreover, we show that the power-law exponent is proportional to
the effective Planck constant h.Comment: 4 pages, 2 figure
Расчет распределения температуры по поверхности низкотемпературного композиционного электрообогревателя для предприятий агропромышленного комплекса
Получены аналитические зависимости и приведены результаты расчета численных значений распределения температур по поверхности низкотемпературного композиционного электрообогревателя, которые могут быть использованы при проектировании аналогичных изделий в различных областях сельского хозяйства и промышленности
Dynamical tunneling in mushroom billiards
We study the fundamental question of dynamical tunneling in generic
two-dimensional Hamiltonian systems by considering regular-to-chaotic tunneling
rates. Experimentally, we use microwave spectra to investigate a mushroom
billiard with adjustable foot height. Numerically, we obtain tunneling rates
from high precision eigenvalues using the improved method of particular
solutions. Analytically, a prediction is given by extending an approach using a
fictitious integrable system to billiards. In contrast to previous approaches
for billiards, we find agreement with experimental and numerical data without
any free parameter.Comment: 4 pages, 4 figure
Expanded boundary integral method and chaotic time-reversal doublets in quantum billiards
We present the expanded boundary integral method for solving the planar
Helmholtz problem, which combines the ideas of the boundary integral method and
the scaling method and is applicable to arbitrary shapes. We apply the method
to a chaotic billiard with unidirectional transport, where we demonstrate
existence of doublets of chaotic eigenstates, which are quasi-degenerate due to
time-reversal symmetry, and a very particular level spacing distribution that
attains a chaotic Shnirelman peak at short energy ranges and exhibits GUE-like
statistics for large energy ranges. We show that, as a consequence of such
particular level statistics or algebraic tunneling between disjoint chaotic
components connected by time-reversal operation, the system exhibits quantum
current reversals.Comment: 18 pages, 8 figures, with 3 additional GIF animations available at
http://chaos.fiz.uni-lj.si/~veble/boundary
Hall Probe Bench for Cryogenic In Vacuum Undulator
The Helmholtz Zentrum Berlin HZB builds a 2m long in vacuum Hall probe measuring bench for the characterization of several in vacuum cryogenic undulators currently under development. Aceurate local magnetic measurements need a positioning control of about 5 Jlll. Fabrication tolerances and potentially strong temperature gradients require an active correction of the Hall probe movement along a straight line. The HZBbench employs a system of Iaser interferometers and positionsensitive detectors, which are used in a feed back loop for the Hall probe position and orientatio
Correlations between spectra with different symmetry: any chance to be observed?
A standard assumption in quantum chaology is the absence of correlation
between spectra pertaining to different symmetries. Doubts were raised about
this statement for several reasons, in particular, because in semiclassics
spectra of different symmetry are expressed in terms of the same set of
periodic orbits. We reexamine this question and find absence of correlation in
the universal regime. In the case of continuous symmetry the problem is reduced
to parametric correlation, and we expect correlations to be present up to a
certain time which is essentially classical but larger than the ballistic time
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