1,614 research outputs found
Calculation of Superdiffusion for the Chirikov-Taylor Model
It is widely known that the paradigmatic Chirikov-Taylor model presents
enhanced diffusion for specific intervals of its stochasticity parameter due to
islands of stability, which are elliptic orbits surrounding accelerator mode
fixed points. In contrast with normal diffusion, its effect has never been
analytically calculated. Here, we introduce a differential form for the
Perron-Frobenius evolution operator in which normal diffusion and
superdiffusion are treated separately through phases formed by angular wave
numbers. The superdiffusion coefficient is then calculated analytically
resulting in a Schloemilch series with an exponent for the
divergences. Numerical simulations support our results.Comment: 4 pages, 2 figures (revised version
Validity of the CAGE in Screening for Problem Drinking in College Students
This item is copyright by the Johns Hopkins University Press.No abstract is available for this item
Delocalization transition of a small number of particles in a box with periodic boundary conditions
We perform molecular dynamics simulation of a small number of particles in a
box with periodic boundary conditions from a view point of chaotic dynamical
systems. There is a transition at a critical energy E_c that each particle is
confined in each unit cell for E<E_c, and the chaotic diffusion occurs for
E>E_c. We find an anomalous behavior of the jump frequency above the critical
energy in a two-particle system, which is related with the infinitely
alternating stability change of the straight motion passing through a saddle
point. We find simultaneous jump motions just above the critical energy in a
four-particle system and sixteen-particle system, which is also related with
the motion passing through the saddle point.Comment: 9 pages, 10 figure
Production of Enhanced Beam Halos via Collective Modes and Colored Noise
We investigate how collective modes and colored noise conspire to produce a
beam halo with much larger amplitude than could be generated by either
phenomenon separately. The collective modes are lowest-order radial eigenmodes
calculated self-consistently for a configuration corresponding to a
direct-current, cylindrically symmetric, warm-fluid Kapchinskij-Vladimirskij
equilibrium. The colored noise arises from unavoidable machine errors and
influences the internal space-charge force. Its presence quickly launches
statistically rare particles to ever-growing amplitudes by continually kicking
them back into phase with the collective-mode oscillations. The halo amplitude
is essentially the same for purely radial orbits as for orbits that are
initially purely azimuthal; orbital angular momentum has no statistically
significant impact. Factors that do have an impact include the amplitudes of
the collective modes and the strength and autocorrelation time of the colored
noise. The underlying dynamics ensues because the noise breaks the
Kolmogorov-Arnol'd-Moser tori that otherwise would confine the beam. These tori
are fragile; even very weak noise will eventually break them, though the time
scale for their disintegration depends on the noise strength. Both collective
modes and noise are therefore centrally important to the dynamics of halo
formation in real beams.Comment: For full resolution pictures please go to
http://www.nicadd.niu.edu/research/beams
Fractal Weyl law for chaotic microcavities: Fresnel's laws imply multifractal scattering
We demonstrate that the harmonic inversion technique is a powerful tool to
analyze the spectral properties of optical microcavities. As an interesting
example we study the statistical properties of complex frequencies of the fully
chaotic microstadium. We show that the conjectured fractal Weyl law for open
chaotic systems [W. T. Lu, S. Sridhar, and M. Zworski, Phys. Rev. Lett. 91,
154101 (2003)] is valid for dielectric microcavities only if the concept of the
chaotic repeller is extended to a multifractal by incorporating Fresnel's laws.Comment: 8 pages, 12 figure
The phase plane of moving discrete breathers
We study anharmonic localization in a periodic five atom chain with
quadratic-quartic spring potential. We use discrete symmetries to eliminate the
degeneracies of the harmonic chain and easily find periodic orbits. We apply
linear stability analysis to measure the frequency of phonon-like disturbances
in the presence of breathers and to analyze the instabilities of breathers. We
visualize the phase plane of breather motion directly and develop a technique
for exciting pinned and moving breathers. We observe long-lived breathers that
move chaotically and a global transition to chaos that prevents forming moving
breathers at high energies.Comment: 8 pages text, 4 figures, submitted to Physical Review Letters. See
http://www.msc.cornell.edu/~houle/localization
Surface Critical Behavior of Binary Alloys and Antiferromagnets: Dependence of the Universality Class on Surface Orientation
The surface critical behavior of semi-infinite
(a) binary alloys with a continuous order-disorder transition and
(b) Ising antiferromagnets in the presence of a magnetic field is considered.
In contrast to ferromagnets, the surface universality class of these systems
depends on the orientation of the surface with respect to the crystal axes.
There is ordinary and extraordinary surface critical behavior for orientations
that preserve and break the two-sublattice symmetry, respectively. This is
confirmed by transfer-matrix calculations for the two-dimensional
antiferromagnet and other evidence.Comment: Final version that appeared in PRL, some minor stylistic changes and
one corrected formula; 4 pp., twocolumn, REVTeX, 3 eps fig
Phase Space Formulation of Quantum Mechanics. Insight into the Measurement Problem
A phase space mathematical formulation of quantum mechanical processes
accompanied by and ontological interpretation is presented in an axiomatic
form. The problem of quantum measurement, including that of quantum state
filtering, is treated in detail. Unlike standard quantum theory both quantum
and classical measuring device can be accommodated by the present approach to
solve the quantum measurement problemComment: 29 pages, 4 figure
Generic spectral properties of right triangle billiards
This article presents a new method to calculate eigenvalues of right triangle
billiards. Its efficiency is comparable to the boundary integral method and
more recently developed variants. Its simplicity and explicitness however allow
new insight into the statistical properties of the spectra. We analyse
numerically the correlations in level sequences at high level numbers (>10^5)
for several examples of right triangle billiards. We find that the strength of
the correlations is closely related to the genus of the invariant surface of
the classical billiard flow. Surprisingly, the genus plays and important role
on the quantum level also. Based on this observation a mechanism is discussed,
which may explain the particular quantum-classical correspondence in right
triangle billiards. Though this class of systems is rather small, it contains
examples for integrable, pseudo integrable, and non integrable (ergodic,
mixing) dynamics, so that the results might be relevant in a more general
context.Comment: 18 pages, 8 eps-figures, revised: stylistic changes, improved
presentatio
- …