244 research outputs found
Complex paths for regular-to-chaotic tunneling rates
In generic Hamiltonian systems tori of regular motion are dynamically
separated from regions of chaotic motion in phase space. Quantum mechanically
these phase-space regions are coupled by dynamical tunneling. We introduce a
semiclassical approach based on complex paths for the prediction of dynamical
tunneling rates from regular tori to the chaotic region. This approach is
demonstrated for the standard map giving excellent agreement with numerically
determined tunneling rates.Comment: 5 pages, 4 figure
Tunneling Mechanism due to Chaos in a Complex Phase Space
We have revealed that the barrier-tunneling process in non-integrable systems
is strongly linked to chaos in complex phase space by investigating a simple
scattering map model. The semiclassical wavefunction reproduces complicated
features of tunneling perfectly and it enables us to solve all the reasons why
those features appear in spite of absence of chaos on the real plane.
Multi-generation structure of manifolds, which is the manifestation of
complex-domain homoclinic entanglement created by complexified classical
dynamics, allows a symbolic coding and it is used as a guiding principle to
extract dominant complex trajectories from all the semiclassical candidates.Comment: 4 pages, RevTeX, 6 figures, to appear in Phys. Rev.
Semiclassical Study on Tunneling Processes via Complex-Domain Chaos
We investigate the semiclassical mechanism of tunneling process in
non-integrable systems. The significant role of complex-phase-space chaos in
the description of the tunneling process is elucidated by studying a simple
scattering map model. Behaviors of tunneling orbits are encoded into symbolic
sequences based on the structure of complex homoclinic tanglement. By means of
the symbolic coding, the phase space itineraries of tunneling orbits are
related with the amounts of imaginary parts of actions gained by the orbits, so
that the systematic search of significant tunneling orbits becomes possible.Comment: 26 pages, 28 figures, submitted to Physical Review
Virtual turning points and bifurcation of Stokes curves for higher order ordinary differential equations
For a higher order linear ordinary differential operator P, its Stokes curve
bifurcates in general when it hits another turning point of P. This phenomenon
is most neatly understandable by taking into account Stokes curves emanating
from virtual turning points, together with those from ordinary turning points.
This understanding of the bifurcation of a Stokes curve plays an important role
in resolving a paradox recently found in the Noumi-Yamada system, a system of
linear differential equations associated with the fourth Painleve equation.Comment: 7 pages, 4 figure
Recovery of chaotic tunneling due to destruction of dynamical localization by external noise
Quantum tunneling in the presence of chaos is analyzed, focusing especially
on the interplay between quantum tunneling and dynamical localization. We
observed flooding of potentially existing tunneling amplitude by adding noise
to the chaotic sea to attenuate the destructive interference generating
dynamical localization. This phenomenon is related to the nature of complex
orbits describing tunneling between torus and chaotic regions. The tunneling
rate is found to obey a perturbative scaling with noise intensity when the
noise intensity is sufficiently small and then saturate in a large noise
intensity regime. A relation between the tunneling rate and the localization
length of the chaotic states is also demonstrated. It is shown that due to the
competition between dynamical tunneling and dynamical localization, the
tunneling rate is not a monotonically increasing function of Planck's constant.
The above results are obtained for a system with a sharp border between torus
and chaotic regions. The validity of the results for a system with a smoothed
border is also explained.Comment: 14 pages, 15 figure
Quantum Dynamics of Atom-molecule BECs in a Double-Well Potential
We investigate the dynamics of two-component Bose-Josephson junction composed
of atom-molecule BECs. Within the semiclassical approximation, the multi-degree
of freedom of this system permits chaotic dynamics, which does not occur in
single-component Bose-Josephson junctions. By investigating the level
statistics of the energy spectra using the exact diagonalization method, we
evaluate whether the dynamics of the system is periodic or non-periodic within
the semiclassical approximation. Additionally, we compare the semiclassical and
full-quantum dynamics.Comment: to appear in JLTP - QFS 200
Evanescent wave approach to diffractive phenomena in convex billiards with corners
What we are going to call in this paper "diffractive phenomena" in billiards
is far from being deeply understood. These are sorts of singularities that, for
example, some kind of corners introduce in the energy eigenfunctions. In this
paper we use the well-known scaling quantization procedure to study them. We
show how the scaling method can be applied to convex billiards with corners,
taking into account the strong diffraction at them and the techniques needed to
solve their Helmholtz equation. As an example we study a classically
pseudointegrable billiard, the truncated triangle. Then we focus our attention
on the spectral behavior. A numerical study of the statistical properties of
high-lying energy levels is carried out. It is found that all computed
statistical quantities are roughly described by the so-called semi-Poisson
statistics, but it is not clear whether the semi-Poisson statistics is the
correct one in the semiclassical limit.Comment: 7 pages, 8 figure
Nambu-Hamiltonian flows associated with discrete maps
For a differentiable map that has
an inverse, we show that there exists a Nambu-Hamiltonian flow in which one of
the initial value, say , of the map plays the role of time variable while
the others remain fixed. We present various examples which exhibit the map-flow
correspondence.Comment: 19 page
Semiclassical Description of Tunneling in Mixed Systems: The Case of the Annular Billiard
We study quantum-mechanical tunneling between symmetry-related pairs of
regular phase space regions that are separated by a chaotic layer. We consider
the annular billiard, and use scattering theory to relate the splitting of
quasi-degenerate states quantized on the two regular regions to specific paths
connecting them. The tunneling amplitudes involved are given a semiclassical
interpretation by extending the billiard boundaries to complex space and
generalizing specular reflection to complex rays. We give analytical
expressions for the splittings, and show that the dominant contributions come
from {\em chaos-assisted}\/ paths that tunnel into and out of the chaotic
layer.Comment: 4 pages, uuencoded postscript file, replaces a corrupted versio
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