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 adde

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 $\Gamma_0$ and transition angular frequency $\omega_A$. 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 $\tau = t\Gamma_0$ of spontaneous emission, we obtain deviations from exponential decay of the form ${\cal O} (1/\tau)$ for the decay amplitude as well as the previously obtained asymptotic behaviors of the form ${\cal O} (1/\tau^2)$ or ${\cal O} (1/\tau \ln^2\tau)$ for $\tau \gg 1$. 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 $\tau$ and for a sufficiently large value of the required angular frequency cut-off $\omega_c$ of the electro-magnetic fluctuations, i.e. $\omega_c \gg \omega_A$, one obtains either a ${\cal O} (1/\tau)$ or a ${\cal O} (1/\tau^2)$ 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