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

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

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

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

I2PA, U-prove, and Idemix: An Evaluation of Memory Usage and Computing Time Efficiency in an IoT Context

The Internet of Things (IoT), in spite of its innumerable advantages, brings many challenges namely issues about users' privacy preservation and constraints about lightweight cryptography. Lightweight cryptography is of capital importance since IoT devices are qualified to be resource-constrained. To address these challenges, several Attribute-Based Credentials (ABC) schemes have been designed including I2PA, U-prove, and Idemix. Even though these schemes have very strong cryptographic bases, their performance in resource-constrained devices is a question that deserves special attention. This paper aims to conduct a performance evaluation of these schemes on issuance and verification protocols regarding memory usage and computing time. Recorded results show that both I2PA and U-prove present very interesting results regarding memory usage and computing time while Idemix presents very low performance with regard to computing time

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.

The Epsilon Calculus and Herbrand Complexity

Hilbert's epsilon-calculus is based on an extension of the language of predicate logic by a term-forming operator $\epsilon_{x}$. Two fundamental results about the epsilon-calculus, the first and second epsilon theorem, play a role similar to that which the cut-elimination theorem plays in sequent calculus. In particular, Herbrand's Theorem is a consequence of the epsilon theorems. The paper investigates the epsilon theorems and the complexity of the elimination procedure underlying their proof, as well as the length of Herbrand disjunctions of existential theorems obtained by this elimination procedure.Comment: 23 p

Rydberg Wave Packets are Squeezed States

We point out that Rydberg wave packets (and similar ``coherent" molecular packets) are, in general, squeezed states, rather than the more elementary coherent states. This observation allows a more intuitive understanding of their properties; e.g., their revivals.Comment: 7 pages of text plus one figure available in the literature, LA-UR 93-2804, to be published in Quantum Optics, LaTe

Radial Squeezed States and Rydberg Wave Packets

We outline an analytical framework for the treatment of radial Rydberg wave packets produced by short laser pulses in the absence of external electric and magnetic fields. Wave packets of this type are localized in the radial coordinates and have p-state angular distributions. We argue that they can be described by a particular analytical class of squeezed states, called radial squeezed states. For hydrogenic Rydberg atoms, we discuss the time evolution of the corresponding hydrogenic radial squeezed states. They are found to undergo decoherence and collapse, followed by fractional and full revivals. We also present their uncertainty product and uncertainty ratio as functions of time. Our results show that hydrogenic radial squeezed states provide a suitable analytical description of hydrogenic Rydberg atoms excited by short-pulsed laser fields.Comment: published in Physical Review

Elliptical Squeezed States and Rydberg Wave Packets

We present a theoretical construction for closest-to-classical wave packets localized in both angular and radial coordinates and moving on a keplerian orbit. The method produces a family of elliptical squeezed states for the planar Coulomb problem that minimize appropriate uncertainty relations in radial and angular coordinates. The time evolution of these states is studied for orbits with different semimajor axes and eccentricities. The elliptical squeezed states may be useful for a description of the motion of Rydberg wave packets excited by short-pulsed lasers in the presence of external fields, which experiments are attempting to produce. We outline an extension of the method to include certain effects of quantum defects appearing in the alkali-metal atoms used in experiments.Comment: published in Phys. Rev. A, vol. 52, p. 2234, Sept. 199