230 research outputs found
Winning Cores in Parity Games
We introduce the novel notion of winning cores in parity games and develop a
deterministic polynomial-time under-approximation algorithm for solving parity
games based on winning core approximation. Underlying this algorithm are a
number properties about winning cores which are interesting in their own right.
In particular, we show that the winning core and the winning region for a
player in a parity game are equivalently empty. Moreover, the winning core
contains all fatal attractors but is not necessarily a dominion itself.
Experimental results are very positive both with respect to quality of
approximation and running time. It outperforms existing state-of-the-art
algorithms significantly on most benchmarks
Coherent states for the hydrogen atom
We construct a system of coherent states for the hydrogen atom that is
expressed in terms of elementary functions. Unlike to the previous attempts in
this direction, this system possesses the properties equivalent to the most of
those for the harmonic oscillator, with modifications due to the character of
the problem.Comment: 6 pages, LATEX, using ioplppt.sty and iopfts.sty. v.2: some misprints
are corrected. To appear in J.Phys.
Aggregation of chemotactic organisms in a differential flow
We study the effect of advection on the aggregation and pattern formation in
chemotactic systems described by Keller-Segel type models. The evolution of
small perturbations is studied analytically in the linear regime complemented
by numerical simulations. We show that a uniform differential flow can
significantly alter the spatial structure and dynamics of the chemotactic
system. The flow leads to the formation of anisotropic aggregates that move
following the direction of the flow, even when the chemotactic organisms are
not directly advected by the flow. Sufficiently strong advection can stop the
aggregation and coarsening process that is then restricted to the direction
perpendicular to the flow
Dependence Logic with Generalized Quantifiers: Axiomatizations
We prove two completeness results, one for the extension of dependence logic
by a monotone generalized quantifier Q with weak interpretation, weak in the
meaning that the interpretation of Q varies with the structures. The second
result considers the extension of dependence logic where Q is interpreted as
"there exists uncountable many." Both of the axiomatizations are shown to be
sound and complete for FO(Q) consequences.Comment: 17 page
Elastic scattering losses in the four-wave mixing of Bose Einstein Condensates
We introduce a classical stochastic field method that accounts for the
quantum fluctuations responsible for spontaneous initiation of various atom
optics processes. We assume a delta-correlated Gaussian noise in all initially
empty modes of atomic field. Its strength is determined by comparison with the
analytical results for two colliding condensates in the low loss limit. Our
method is applied to the atomic four wave mixing experiment performed at MIT
[Vogels {\it et. al.}, Phys. Rev. Lett. {\bf 89}, 020401, (2002)], for the
first time reproducing experimental data
Hydrogen atom in phase space: The Wigner representation
We have found an effective method of calculating the Wigner function, being a
quantum analogue of joint probability distribution of position and momentum,
for bound states of nonrelativistic hydrogen atom. The formal similarity
between the eigenfunctions of nonrelativistic hydrogen atom in the momentum
representation and Klein-Gordon propagators has allowed the calculation of the
Wigner function for an arbitrary bound state of the hydrogen atom. These Wigner
functions for some low lying states are depicted and discussed.Comment: 8 pages (including figures
Coherent states for the hydrogen atom
We construct wave packets for the hydrogen atom labelled by the classical
action-angle variables with the following properties. i) The time evolution is
exactly given by classical evolution of the angle variables. (The angle
variable corresponding to the position on the orbit is now non-compact and we
do not get exactly the same state after one period. However the gross features
do not change. In particular the wave packet remains peaked around the labels.)
ii) Resolution of identity using this overcomplete set involves exactly the
classical phase space measure. iii) Semi-classical limit is related to
Bohr-Sommerfield quantization. iv) They are almost minimum uncertainty wave
packets in position and momentum.Comment: 9 pages, 2 figures, minor change in language and journal reference
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Memory Effects in Spontaneous Emission Processes
We consider a quantum-mechanical analysis of spontaneous emission in terms of
an effective two-level system with a vacuum decay rate and
transition angular frequency . Our analysis is in principle exact,
even though presented as a numerical solution of the time-evolution including
memory effects. The results so obtained are confronted with previous
discussions in the literature. In terms of the {\it dimensionless} lifetime
of spontaneous emission, we obtain deviations from
exponential decay of the form for the decay amplitude as
well as the previously obtained asymptotic behaviors of the form or for . The actual
asymptotic behavior depends on the adopted regularization procedure as well as
on the physical parameters at hand. We show that for any reasonable range of
and for a sufficiently large value of the required angular frequency
cut-off of the electro-magnetic fluctuations, i.e. , one obtains either a or a
dependence. In the presence of physical boundaries, which can change the decay
rate with many orders of magnitude, the conclusions remains the same after a
suitable rescaling of parameters.Comment: 13 pages, 5 figures and 46 reference
Is Schr\"{o}dinger's Conjecture for the Hydrogen Atom Coherent States Attainable
We construct the most general SO(4,2) hydrogen atom coherent states which are
the counterpart of Schr\"{o}dinger's harmonic oscillator coherent states. We
show that these states cannot be localized and cannot follow the classical
orbits. Thus, Schr\"{o}dinger's conjecture for the hydrogen atom coherent
states is unattainable.Comment: 10 pages, report
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