T-matrix formulation of real-space dynamical mean-field theory and the Friedel sum rule for correlated lattice fermions

We formulate real-space dynamical mean-field theory within scattering theory. Thereby the Friedel sum rule is derived for interacting lattice fermions at zero temperature.Comment: 7 pages, no figures, extended and corrected versio

Non-Zero Sum Games for Reactive Synthesis

In this invited contribution, we summarize new solution concepts useful for the synthesis of reactive systems that we have introduced in several recent publications. These solution concepts are developed in the context of non-zero sum games played on graphs. They are part of the contributions obtained in the inVEST project funded by the European Research Council.Comment: LATA'16 invited pape

Probing dense matter in neutron stars with axial w-modes

We study the problem of extracting information about composition and equation of state of dense matter in neutron star interior using axial w-modes. We determine complex frequencies of axial w-modes for a set of equations of state involving hyperons as well as Bose-Einstein condensates of antikaons adopting the continued fraction method. Hyperons and antikaon condensates result in softer equations of state leading to higher frequencies of first axial w-modes than that of nuclear matter case, whereas the opposite happens in case of damping times. The presence of condensates may lead to the appearance of a new stable branch of superdense stars beyond the neutron star branch called the third family. The existence of same mass compact stars in both branches are known as neutron star twins. Further investigation of twins reveal that first axial w-mode frequencies of superdense stars in the third family are higher than those of the corresponding twins in the neutron star branch.Comment: LaTeX; 23 pages including two tables and 11 figure

Kaluza-Klein solitons reexamined

In (4 + 1) gravity the assumption that the five-dimensional metric is independent of the fifth coordinate authorizes the extra dimension to be either spacelike or timelike. As a consequence of this, the time coordinate and the extra coordinate are interchangeable, which in turn allows the conception of different scenarios in 4D from a single solution in 5D. In this paper, we make a thorough investigation of all possible 4D scenarios, associated with this interchange, for the well-known Kramer-Gross-Perry-Davidson-Owen set of solutions. We show that there are {\it three} families of solutions with very distinct geometrical and physical properties. They correspond to different sets of values of the parameters which characterize the solutions in 5D. The solutions of physical interest are identified on the basis of physical requirements on the induced-matter in 4D. We find that only one family satisfies these requirements; the other two violate the positivity of mass-energy density. The "physical" solutions possess a lightlike singularity which coincides with the horizon. The Schwarzschild black string solution as well as the zero moment dipole solution of Gross and Perry are obtained in different limits. These are analyzed in the context of Lake's geometrical approach. We demonstrate that the parameters of the solutions in 5D are not free, as previously considered. Instead, they are totally determined by measurements in 4D. Namely, by the surface gravitational potential of the astrophysical phenomena, like the Sun or other stars, modeled in Kaluza-Klein theory. This is an important result which may help in observations for an experimental/observational test of the theory.Comment: In V2 we include an Appendix, where we examine the conformal approach. Minor changes at the beginning of section 2. In V3 more references are added. Minor editorial changes in the Introduction and Conclusions section

Phase transitions in Ising model on a Euclidean network

A one dimensional network on which there are long range bonds at lattice distances $l>1$ with the probability $P(l) \propto l^{-\delta}$ has been taken under consideration. We investigate the critical behavior of the Ising model on such a network where spins interact with these extra neighbours apart from their nearest neighbours for $0 \leq \delta < 2$. It is observed that there is a finite temperature phase transition in the entire range. For $0 \leq \delta < 1$, finite size scaling behaviour of various quantities are consistent with mean field exponents while for $1\leq \delta\leq 2$, the exponents depend on $\delta$. The results are discussed in the context of earlier observations on the topology of the underlying network.Comment: 7 pages, revtex4, 7 figures; to appear in Physical Review E, minor changes mad

Games on graphs with a public signal monitoring

We study pure Nash equilibria in games on graphs with an imperfect monitoring based on a public signal. In such games, deviations and players responsible for those deviations can be hard to detect and track. We propose a generic epistemic game abstraction, which conveniently allows to represent the knowledge of the players about these deviations, and give a characterization of Nash equilibria in terms of winning strategies in the abstraction. We then use the abstraction to develop algorithms for some payoff functions.Comment: 28 page