462 research outputs found
The Arbitrary Trajectory Quantization Method
The arbitrary trajectory quantization method (ATQM) is a time dependent
approach to quasiclassical quantization based on the approximate dual
relationship that exists between the quantum energy spectra and classical
periodic orbits. It has recently been shown however, that, for polygonal
billiards, the periodicity criterion must be relaxed to include closed
almost-periodic (CAP) orbit families in this relationship. In light of this
result, we reinvestigate the ATQM and show that at finite energies, a
smoothened quasiclassical kernel corresponds to the modified formula that
includes CAP families while the delta function kernel corresponding to the
periodic orbit formula is recovered at high energies. Several clarifications
are also provided.Comment: revtex, ps figure
Localization properties of groups of eigenstates in chaotic systems
In this paper we study in detail the localized wave functions defined in
Phys. Rev. Lett. {\bf 76}, 1613 (1994), in connection with the scarring effect
of unstable periodic orbits in highly chaotic Hamiltonian system. These
functions appear highly localized not only along periodic orbits but also on
the associated manifolds. Moreover, they show in phase space the hyperbolic
structure in the vicinity of the orbit, something which translates in
configuration space into the structure induced by the corresponding self--focal
points. On the other hand, the quantum dynamics of these functions are also
studied. Our results indicate that the probability density first evolves along
the unstable manifold emanating from the periodic orbit, and localizes
temporarily afterwards on only a few, short related periodic orbits. We believe
that this type of studies can provide some keys to disentangle the complexity
associated to the quantum mechanics of these kind of systems, which permits the
construction of a simple explanation in terms of the dynamics of a few
classical structures.Comment: 9 pages, 8 Postscript figures (low resolution). For high resolution
versions of figs http://www.tandar.cnea.gov.ar/~wisniack/ To appear in Phys.
Rev.
Uniform semiclassical wave function for coherent 2D electron flow
We find a uniform semiclassical (SC) wave function describing coherent
branched flow through a two-dimensional electron gas (2DEG), a phenomenon
recently discovered by direct imaging of the current using scanned probed
microscopy. The formation of branches has been explained by classical
arguments, but the SC simulations necessary to account for the coherence are
made difficult by the proliferation of catastrophes in the phase space. In this
paper, expansion in terms of "replacement manifolds" is used to find a uniform
SC wave function for a cusp singularity. The method is then generalized and
applied to calculate uniform wave functions for a quantum-map model of coherent
flow through a 2DEG. Finally, the quantum-map approximation is dropped and the
method is shown to work for a continuous-time model as well.Comment: 9 pages, 7 figure
Numerical study of scars in a chaotic billiard
We study numerically the scaling properties of scars in stadium billiard.
Using the semiclassical criterion, we have searched systematically the scars of
the same type through a very wide range, from ground state to as high as the 1
millionth state. We have analyzed the integrated probability density along the
periodic orbit. The numerical results confirm that the average intensity of
certain types of scars is independent of rather than scales with
. Our findings confirm the theoretical predictions of Robnik
(1989).Comment: 7 pages in Revtex 3.1, 5 PS figures available upon request. To appear
in Phys. Rev. E, Vol. 55, No. 5, 199
Scarred Patterns in Surface Waves
Surface wave patterns are investigated experimentally in a system geometry
that has become a paradigm of quantum chaos: the stadium billiard. Linear waves
in bounded geometries for which classical ray trajectories are chaotic are
known to give rise to scarred patterns. Here, we utilize parametrically forced
surface waves (Faraday waves), which become progressively nonlinear beyond the
wave instability threshold, to investigate the subtle interplay between
boundaries and nonlinearity. Only a subset (three main types) of the computed
linear modes of the stadium are observed in a systematic scan. These correspond
to modes in which the wave amplitudes are strongly enhanced along paths
corresponding to certain periodic ray orbits. Many other modes are found to be
suppressed, in general agreement with a prediction by Agam and Altshuler based
on boundary dissipation and the Lyapunov exponent of the associated orbit.
Spatially asymmetric or disordered (but time-independent) patterns are also
found even near onset. As the driving acceleration is increased, the
time-independent scarred patterns persist, but in some cases transitions
between modes are noted. The onset of spatiotemporal chaos at higher forcing
amplitude often involves a nonperiodic oscillation between spatially ordered
and disordered states. We characterize this phenomenon using the concept of
pattern entropy. The rate of change of the patterns is found to be reduced as
the state passes temporarily near the ordered configurations of lower entropy.
We also report complex but highly symmetric (time-independent) patterns far
above onset in the regime that is normally chaotic.Comment: 9 pages, 10 figures (low resolution gif files). Updated and added
references and text. For high resolution images:
http://physics.clarku.edu/~akudrolli/stadium.htm
Influence of cardiac autonomic neuropathy on cardiac repolarisation during incremental adrenaline infusion in type 1 diabetes
Aims/hypothesis
We examined the effect of a standardised sympathetic stimulus, incremental adrenaline (epinephrine) infusion on cardiac repolarisation in individuals with type 1 diabetes with normal autonomic function, subclinical autonomic neuropathy and established autonomic neuropathy.
Methods
Ten individuals with normal autonomic function and baroreceptor sensitivity tests (NAF), seven with subclinical autonomic neuropathy (SAN; normal standard autonomic function tests and abnormal baroreceptor sensitivity tests); and five with established cardiac autonomic neuropathy (CAN; abnormal standard autonomic function and baroreceptor tests) underwent an incremental adrenaline infusion. Saline (0.9% NaCl) was infused for the first hour followed by 0.01 ÎŒg kgâ1 minâ1 and 0.03 ÎŒg kgâ1 minâ1 adrenaline for the second and third hours, respectively, and 0.06 ÎŒg kgâ1 minâ1 for the final 30 min. High resolution ECG monitoring for QTc duration, ventricular repolarisation parameters (T wave amplitude, T wave area symmetry ratio) and blood sampling for potassium and catecholamines was performed every 30 min.
Results
Baseline heart rate was 68 (95% CI 60, 76) bpm for the NAF group, 73 (59, 87) bpm for the SAN group and 84 (78, 91) bpm for the CAN group. During adrenaline infusion the heart rate increased differently across the groups (pâ=â0.01). The maximum increase from baseline (95% CI) in the CAN group was 22 (13, 32) bpm compared with 11 (7, 15) bpm in the NAF and 10 (3, 18) bpm in the SAN groups. Baseline QTc was 382 (95% CI 374, 390) ms in the NAF, 378 (363, 393) ms in the SAN and 392 (367, 417) ms in the CAN groups (pâ=â0.31). QTc in all groups lengthened comparably with adrenaline infusion. The longest QTc was 444 (422, 463) ms (NAF), 422 (402, 437) ms (SAN) and 470 (402, 519) ms (CAN) (pâ=â0.09). T wave amplitude and T wave symmetry ratio decreased and the maximum decrease occurred earlier, at lower infused adrenaline concentrations in the CAN group compared with NAF and SAN groups. AUC for the symmetry ratio was different across the groups and was lowest in the CAN group (pâ=â0.04). Plasma adrenaline rose and potassium fell comparably in all groups.
Conclusions/interpretation
Participants with CAN showed abnormal repolarisation in some measures at lower adrenaline concentrations. This may be due to denervation adrenergic hypersensitivity. Such individuals may be at greater risk of cardiac arrhythmias in response to physiological sympathoadrenal challenges such as stress or hypoglycaemia
Statistics of pre-localized states in disordered conductors
The distribution function of local amplitudes of single-particle states in
disordered conductors is calculated on the basis of the supersymmetric
-model approach using a saddle-point solution of its reduced version.
Although the distribution of relatively small amplitudes can be approximated by
the universal Porter-Thomas formulae known from the random matrix theory, the
statistics of large amplitudes is strongly modified by localization effects. In
particular, we find a multifractal behavior of eigenstates in 2D conductors
which follows from the non-integer power-law scaling for the inverse
participation numbers (IPN) with the size of the system. This result is valid
for all fundamental symmetry classes (unitary, orthogonal and symplectic). The
multifractality is due to the existence of pre-localized states which are
characterized by power-law envelopes of wave functions, , . The pre-localized states in short quasi-1D wires have the
power-law tails , too, although their IPN's
indicate no fractal behavior. The distribution function of the
largest-amplitude fluctuations of wave functions in 2D and 3D conductors has
logarithmically-normal asymptotics.Comment: RevTex, 17 twocolumn pages; revised version (several misprint
corrected
Postmodern String Theory: Stochastic Formulation
In this paper we study the dynamics of a statistical ensemble of strings,
building on a recently proposed gauge theory of the string geodesic field. We
show that this stochastic approach is equivalent to the Carath\'eodory
formulation of the Nambu-Goto action, supplemented by an averaging procedure
over the family of classical string world-sheets which are solutions of the
equation of motion. In this new framework, the string geodesic field is
reinterpreted as the Gibbs current density associated with the string
statistical ensemble. Next, we show that the classical field equations derived
from the string gauge action, can be obtained as the semi-classical limit of
the string functional wave equation. For closed strings, the wave equation
itself is completely analogous to the Wheeler-DeWitt equation used in quantum
cosmology. Thus, in the string case, the wave function has support on the space
of all possible spatial loop configurations. Finally, we show that the string
distribution induces a multi-phase, or {\it cellular} structure on the
spacetime manifold characterized by domains with a purely Riemannian geometry
separated by domain walls over which there exists a predominantly Weyl
geometry.Comment: 24pages, ReVTe
Chaos Driven Decay of Nuclear Giant Resonances: Route to Quantum Self-Organization
The influence of background states with increasing level of complexity on the
strength distribution of the isoscalar and isovector giant quadrupole resonance
in Ca is studied. It is found that the background characteristics,
typical for chaotic systems, strongly affects the fluctuation properties of the
strength distribution. In particular, the small components of the wave function
obey a scaling law analogous to self-organized systems at the critical state.
This appears to be consistent with the Porter-Thomas distribution of the
transition strength.Comment: 14 pages, 4 Figures, Illinois preprint P-93-12-106, Figures available
from the author
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