2,246,969 research outputs found
Dynamical Tunneling in Mixed Systems
We study quantum-mechanical tunneling in mixed dynamical systems between
symmetry-related phase space tori separated by a chaotic layer. Considering
e.g. the annular billiard we decompose tunneling-related energy splittings and
shifts into sums over paths in phase space. We show that tunneling transport is
dominated by chaos-assisted paths that tunnel into and out of the chaotic layer
via the ``beach'' regions sandwiched between the regular islands and the
chaotic sea. Level splittings are shown to fluctuate on two scales as functions
of energy or an external parameter: they display a dense sequence of peaks due
to resonances with states supported by the chaotic sea, overlaid on top of slow
modulations arising from resonances with states supported by the ``beaches''.
We obtain analytic expressions which enable us to assess the relative
importance of tunneling amplitudes into the chaotic sea vs. its internal
transport properties. Finally, we average over the statistics of the chaotic
region, and derive the asymptotic tail of the splitting distribution function
under rather general assumptions concerning the fluctuation properties of
chaotic states.Comment: 28 pages, Latex, 16 EPS figure
Discrete port-Hamiltonian systems: mixed interconnections
Either from a control theoretic viewpoint or from an analysis viewpoint it is necessary to convert smooth systems to discrete systems, which can then be implemented on computers for numerical simulations. Discrete models can be obtained either by discretizing a smooth model, or by directly modeling at the discrete level itself. The goal of this paper is to apply a previously developed discrete modeling technique to study the interconnection of continuous systems with discrete ones in such a way that passivity is preserved. Such a theory has potential applications, in the field of haptics, telemanipulation etc. It is shown that our discrete modeling theory can be used to formalize previously developed techniques for obtaining passive interconnections of continuous and discrete systems
Regular Tunnelling Sequences in Mixed Systems
We show that the pattern of tunnelling rates can display a vivid and regular
pattern when the classical dynamics is of mixed chaotic/regular type. We
consider the situation in which the dominant tunnelling route connects to a
stable periodic orbit and this orbit is surrounded by a regular island which
supports a number of quantum states. We derive an explicit semiclassical
expression for the positions and tunnelling rates of these states by use of a
complexified trace formula.Comment: submitted to Physica E as a contribution to the workshop proceedings
of "Dynamics of Complex Systems" held at the Max Planck Institute for the
Physics of Complex Systems in Dresden from March 30 to June 15, 199
Refinement for Transition Systems with Responses
Motivated by the response pattern for property specifications and
applications within flexible workflow management systems, we report upon an
initial study of modal and mixed transition systems in which the must
transitions are interpreted as must eventually, and in which implementations
can contain may behaviors that are resolved at run-time. We propose Transition
Systems with Responses (TSRs) as a suitable model for this study. We prove that
TSRs correspond to a restricted class of mixed transition systems, which we
refer to as the action-deterministic mixed transition systems. We show that
TSRs allow for a natural definition of deadlocked and accepting states. We then
transfer the standard definition of refinement for mixed transition systems to
TSRs and prove that refinement does not preserve deadlock freedom. This leads
to the proposal of safe refinements, which are those that preserve deadlock
freedom. We exemplify the use of TSRs and (safe) refinements on a small
medication workflow.Comment: In Proceedings FIT 2012, arXiv:1207.348
Divided executives and democratisation
This article examines the effect of a divided executive on
democratisation in mixed systems where presidents are directly elected and prime ministers are responsible to the legislature. A divided executive is where the president and prime minister are not from the same party. The importance of a divided executive is hypothesised to vary according to the relative powers of the president and prime minister. In mixed systems where either the president or the prime minister is the dominant actor, then a divided executive will not affect democratisation. However, where both the president and prime minister have significant independent
powers, then a divided executive should have a negative impact on democratisation because of the potential for destabilising intraexecutive conflict. Using an ordinal logit model, the results show that mixed systems with a dual executive do not perform significantly worse than mixed systems where there is one dominant actor. This suggests that the standard wisdom about the impact of a divided executive in a mixed system is misplaced
Variational Principle for Mixed Classical-Quantum Systems
An extended variational principle providing the equations of motion for a
system consisting of interacting classical, quasiclassical and quantum
components is presented, and applied to the model of bilinear coupling. The
relevant dynamical variables are expressed in the form of a quantum state
vector which includes the action of the classical subsystem in its phase
factor. It is shown that the statistical ensemble of Brownian state vectors for
a quantum particle in a classical thermal environment can be described by a
density matrix evolving according to a nonlinear quantum Fokker-Planck
equation. Exact solutions of this equation are obtained for a two-level system
in the limit of high temperatures, considering both stationary and
nonstationary initial states. A treatment of the common time shared by the
quantum system and its classical environment, as a collective variable rather
than as a parameter, is presented in the Appendix.Comment: 16 pages, LaTex; added Figure 2 and Figure
Amplitude distribution of eigenfunctions in mixed systems
We study the amplitude distribution of irregular eigenfunctions in systems
with mixed classical phase space. For an appropriately restricted random wave
model a theoretical prediction for the amplitude distribution is derived and
good agreement with numerical computations for the family of limacon billiards
is found. The natural extension of our result to more general systems, e.g.
with a potential, is also discussed.Comment: 13 pages, 3 figures. Some of the pictures are included in low
resolution only. For a version with pictures in high resolution see
http://www.physik.uni-ulm.de/theo/qc/ or http://www.maths.bris.ac.uk/~maab
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