Ursell operators in statistical physics of dense systems: the role of high order operators and of exchange cycles

The purpose of this article is to discuss cluster expansions in dense quantum systems as well as their interconnection with exchange cycles. We show in general how the Ursell operators of order 3 or more contribute to an exponential which corresponds to a mean-field energy involving the second operator U2, instead of the potential itself as usual. In a first part, we consider classical statistical mechanics and recall the relation between the reducible part of the classical cluster integrals and the mean-field; we introduce an alternative method to obtain the linear density contribution to the mean-field, which is based on the notion of tree-diagrams and provides a preview of the subsequent quantum calculations. We then proceed to study quantum particles with Boltzmann statistics (distinguishable particles) and show that each Ursell operator Un with n greater or equal to 3 contains a ``tree-reducible part'', which groups naturally with U2 through a linear chain of binary interactions; this part contributes to the associated mean-field experienced by particles in the fluid. The irreducible part, on the other hand, corresponds to the effects associated with three (or more) particles interacting all together at the same time. We then show that the same algebra holds in the case of Fermi or Bose particles, and discuss physically the role of the exchange cycles, combined with interactions. Bose condensed systems are not considered at this stage. The similarities and differences between Boltzmann and quantum statistics are illustrated by this approach, in contrast with field theoretical or Green's functions methods, which do not allow a separate study of the role of quantum statistics and dynamics.Comment: 31 pages, 7 figure

Testing for lack of fit in inverse regression - with applications to photonic imaging.

Regression; Problems; Lack-of-fit; Applications;

Security Attributes Based Digital Rights Management

Most real-life systems delegate responsibilities to different authorities. We apply this model to a digital rights management system, to achieve flexible security. In our model a hierarchy of authorities issues certificates that are linked by cryptographic means. This linkage establishes a chain of control, identity-attribute-rights, and allows flexible rights control over content. Typical security objectives, such as identification, authentication, authorization and access control can be realised. Content keys are personalised to detect illegal super distribution. We describe a working prototype, which we develop using standard techniques, such as standard certificates, XML and Java. We present experimental results to evaluate the scalability of the system. A formal analysis demonstrates that our design is able to detect a form of illegal super distribution

Bose-Einstein transition temperature in a dilute repulsive gas

We discuss certain specific features of the calculation of the critical temperature of a dilute repulsive Bose gas. Interactions modify the critical temperature in two different ways. First, for gases in traps, temperature shifts are introduced by a change of the density profile, arising itself from a modification of the equation of state of the gas (reduced compressibility); these shifts can be calculated simply within mean field theory. Second, even in the absence of a trapping potential (homogeneous gas in a box), temperature shifts are introduced by the interactions; they arise from the correlations introduced in the gas, and thus lie inherently beyond mean field theory - in fact, their evaluation requires more elaborate, non-perturbative, calculations. One illustration of this non-perturbative character is provided by the solution of self-consistent equations, which relate together non-linearly the various energy shifts of the single particle levels k. These equations predict that repulsive interactions shift the critical temperature (at constant density) by an amount which is positive, and simply proportional to the scattering length a; nevertheless, the numerical coefficient is difficult to compute. Physically, the increase of the temperature can be interpreted in terms of the reduced density fluctuations introduced by the repulsive interactions, which facilitate the propagation of large exchange cycles across the sample.Comment: two minor corrections, two refs adde

Universal scaling of the elliptic flow data at RHIC

Recent PHOBOS measurements of the excitation function for the pseudo-rapidity dependence of elliptic flow in Au+Au collisions at RHIC, have posed a significant theoretical challenge. Here we show that these differential measurements, as well as the RHIC measurements on transverse momentum satisfy a universal scaling relation predicted by the Buda-Lund model, based on exact solutions of perfect fluid hydrodynamics. We also show that recently found transverse kinetic energy scaling of the elliptic flow is a special case of this universal scaling.Comment: 4 pages, 3 figures, 1 tabl

Decomposition of Harmonic and Jet Contributions to Particle-pair Correlations at Ultra-relativistic Energies

Methodology is presented for analysis of two-particle azimuthal angle correlation functions obtained in collisions at ultra-relativistic energies. We show that harmonic and di-jet contributions to these correlation functions can be reliably decomposed by two techniques to give an accurate measurement of the jet-pair distribution. Results from detailed Monte Carlo simulations are used to demonstrate the efficacy of these techniques in the study of possible modifications to jet topologies in heavy ion reactions.Comment: Updated version to be published in PRC Rapid Com

Do bilateral social security agreements deliver on the portability of pensions and health care benefits? A summary policy paper on four migration corridors between EU and non-EU member states

This policy paper summarizes four corridor studies on bilateral social security agreements (BSSAs) between four EU Member and two non-Member States, draws conclusions on their results, and offers recommendations. BSSAs between migrant-sending and migrant-receiving countries are seen as the most important instrument to establish portability of social security benefits for internationally mobile workers. Yet only about 23 percent of international migrants profit from BSSAs and their functioning has been little analyzed and even less assessed. The four corridors studied (Austria-Turkey, Germany-Turkey, Belgium-Morocco, and France-Morocco) were selected to allow for comparison of both similarities and differences in experiences. The evaluation of these corridors' BSSAs was undertaken against a methodological framework and three selected criteria: fairness for individuals, fiscal fairness for countries, and bureaucratic effectiveness for countries and migrant workers. The results suggest that the investigated BSSAs work and overall deliver reasonably well on individual fairness. The results on fiscal fairness are clouded by conceptual and empirical gaps. Bureaucratic effectiveness would profit from ICT-based exchanges on both corridors once available

Conserving Gapless Mean-Field Theory for Bose-Einstein Condensates

We formulate a conserving gapless mean-field theory for Bose-Einstein condensates on the basis of a Luttinger-Ward thermodynamic functional. It is applied to a weakly interacting uniform gas with density $n$ and s-wave scattering length $a$ to clarify its fundamental thermodynamic properties. It is found that the condensation here occurs as a first-order transition. The shift of the transition temperature $\Delta T_c$ from the ideal-gas result $T_{0}$ is positive and given to the leading order by $\Delta T_c = 2.33a n^{1/3}T_0$, in agreement with a couple of previous estimates. The theory is expected to form a new theoretical basis for trapped Bose-Einstein condensates at finite temperatures.Comment: Minor errors remove