1,213 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
Weyl law for open systems with sharply divided mixed phase space
A generalization of the Weyl law to systems with a sharply divided mixed
phase space is proposed. The ansatz is composed of the usual Weyl term which
counts the number of states in regular islands and a term associated with
sticky regions in phase space. For a piecewise linear map, we numerically check
the validity of our hypothesis, and find good agreement not only for the case
with a sharply divided phase space, but also for the case where tiny island
chains surround the main regular island. For the latter case, a non-trivial
power law exponent appears in the survival probability of classical escaping
orbits, which may provide a clue to develop the Weyl law for more generic mixed
systems.Comment: 8 pages, 14 figure
How Even Revises Expectation in a Scalar Model: Analogy with Japanese Mo
PACLIC / The University of the Philippines Visayas Cebu College Cebu City, Philippines / November 20-22, 200
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