2,783 research outputs found
Resonance-assisted tunneling in three degrees of freedom without discrete symmetry
We study dynamical tunneling in a near-integrable Hamiltonian with three
degrees of freedom. The model Hamiltonian does not have any discrete symmetry.
Despite this lack of symmetry we show that the mixing of near-degenerate
quantum states is due to dynamical tunneling mediated by the nonlinear
resonances in the classical phase space. Identifying the key resonances allows
us to suppress the dynamical tunneling via the addition of weak
counter-resonant terms.Comment: 4 pages, 4 figures (low resolution
Rotating Accelerator-Mode Islands
The existence of rotating accelerator-mode islands (RAIs), performing
quasiregular motion in rotational resonances of order of the standard
map, is firmly established by an accurate numerical analysis of all the known
data. It is found that many accelerator-mode islands for relatively small
nonintegrability parameter are RAIs visiting resonances of different orders
. For sufficiently large , one finds also ``pure'' RAIs visiting
only resonances of the {\em same} order, or . RAIs, even quite small
ones, are shown to exhibit sufficient stickiness to produce an anomalous
chaotic transport. The RAIs are basically different in nature from
accelerator-mode islands in resonances of the ``forced'' standard map which was
extensively studied recently in the context of quantum accelerator modes.Comment: REVTEX, 31 pages (including 2 tables and 15 figures
Wave packet approach to periodically driven scattering
For autonomous systems it is well known how to extract tunneling
probabilities from wavepacket calculations. Here we present a corresponding
approach for periodically time-dependent Hamiltonians, valid at all
frequencies, field strengths, and transition orders. After mapping the
periodically driven system onto a time-independent one with an additional
degree of freedom, use is made of the correlation function formulation of
scattering [J. Chem. Phys. {\bf 98}, 3884 (1993)]. The formalism is then
applied to study the transmission properties of a resonant tunneling double
barrier structure under the influence of a sinusoidal laser field, revealing an
unexpected antiresonance in the zero photon transition for large field
strengths.Comment: 4 pages, 2 figure
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
Finite times to equipartition in the thermodynamic limit
We study the time scale T to equipartition in a 1D lattice of N masses
coupled by quartic nonlinear (hard) springs (the Fermi-Pasta-Ulam beta model).
We take the initial energy to be either in a single mode gamma or in a package
of low frequency modes centered at gamma and of width delta-gamma, with both
gamma and delta-gamma proportional to N. These initial conditions both give,
for finite energy densities E/N, a scaling in the thermodynamic limit (large
N), of a finite time to equipartition which is inversely proportional to the
central mode frequency times a power of the energy density E/N. A theory of the
scaling with E/N is presented and compared to the numerical results in the
range 0.03 <= E/N <= 0.8.Comment: Plain TeX, 5 `eps' figures, submitted to Phys. Rev.
On the local nature and scaling of chaos in weakly nonlinear disordered chains
The dynamics of a disordered nonlinear chain can be either regular or chaotic
with a certain probability. The chaotic behavior is often associated with the
destruction of Anderson localization by the nonlinearity. In the presentwork it
is argued that at weak nonlinearity chaos is nucleated locally on rare resonant
segments of the chain. Based on this picture, the probability of chaos is
evaluated analytically. The same probability is also evaluated by direct
numerical sampling of disorder realizations and quantitative agreement between
the two results is found
Ray model and ray-wave correspondence in coupled optical microdisks
We introduce a ray model for coupled optical microdisks, in which we select
coupling-efficient rays among the splitting rays. We investigate the resulting
phase-space structure and report island structures arising from the
ray-coupling between the two microdisks. We find the microdisks's refractive
index to influence the phase-space structure and calculate the stability and
decay rates of the islands. Turning to ray-wave correspondence, we find many
resonances to be directly related to the presence of these islands. We study
the relation between the (ray-picture originating) island structures and the
(wave-picture originating) spectral properties of resonances, especially the
leakiness of the resonances which is represented as the imaginary part of the
complex wave vector.Comment: 9 pages, 8 figure
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