Multiple addition theorem for discrete and continuous nonlinear problems

The addition relation for the Riemann theta functions and for its limits, which lead to the appearance of exponential functions in soliton type equations is discussed. The presented form of addition property resolves itself to the factorization of N-tuple product of the shifted functions and it seems to be useful for analysis of soliton type continuous and discrete processes in the N+1 space-time. A close relation with the natural generalization of bi- and tri-linear operators into multiple linear operators concludes the paper.Comment: 9 page

Tests of Basic Quantum Mechanics in Oscillation Experiments

According to standard quantum theory, the time evolution operator of a quantum system is independent of the state of the system. One can, however, consider systems in which this is not the case: the evolution operator may depend on the density operator itself. The presence of such modifications of quantum theory can be tested in long baseline oscillation experiments.Comment: 8 pages, LaTeX; no macros neede

One-loop Beta Functions for the Orientable Non-commutative Gross-Neveu Model

We compute at the one-loop order the beta-functions for a renormalisable non-commutative analog of the Gross Neveu model defined on the Moyal plane. The calculation is performed within the so called x-space formalism. We find that this non-commutative field theory exhibits asymptotic freedom for any number of colors. The beta-function for the non-commutative counterpart of the Thirring model is found to be non vanishing.Comment: 16 pages, 9 figure

Dynamical generalization of a solvable family of two-electron model atoms with general interparticle repulsion

Holas, Howard and March [Phys. Lett. A {\bf 310}, 451 (2003)] have obtained analytic solutions for ground-state properties of a whole family of two-electron spin-compensated harmonically confined model atoms whose different members are characterized by a specific interparticle potential energy u($r_{12}$). Here, we make a start on the dynamic generalization of the harmonic external potential, the motivation being the serious criticism levelled recently against the foundations of time-dependent density-functional theory (e.g. [J. Schirmer and A. Dreuw, Phys. Rev. A {\bf 75}, 022513 (2007)]). In this context, we derive a simplified expression for the time-dependent electron density for arbitrary interparticle interaction, which is fully determined by an one-dimensional non-interacting Hamiltonian. Moreover, a closed solution for the momentum space density in the Moshinsky model is obtained.Comment: 5 pages, submitted to J. Phys.

Causality violation and singularities

We show that singularities necessarily occur when a boundary of causality violating set exists in a space-time under the physically suitable assumptions except the global causality condition in the Hawking-Penrose singularity theorems. Instead of the global causality condition, we impose some restrictions on the causality violating sets to show the occurrence of singularities.Comment: 11 pages, latex, 2 eps figure

Network synchronization: Optimal and Pessimal Scale-Free Topologies

By employing a recently introduced optimization algorithm we explicitely design optimally synchronizable (unweighted) networks for any given scale-free degree distribution. We explore how the optimization process affects degree-degree correlations and observe a generic tendency towards disassortativity. Still, we show that there is not a one-to-one correspondence between synchronizability and disassortativity. On the other hand, we study the nature of optimally un-synchronizable networks, that is, networks whose topology minimizes the range of stability of the synchronous state. The resulting ``pessimal networks'' turn out to have a highly assortative string-like structure. We also derive a rigorous lower bound for the Laplacian eigenvalue ratio controlling synchronizability, which helps understanding the impact of degree correlations on network synchronizability.Comment: 11 pages, 4 figs, submitted to J. Phys. A (proceedings of Complex Networks 2007

M5-brane geometries, T-duality and fluxes

We describe a duality relation between configurations of M5-branes in M-theory and type IIB theory on Taub-NUT geometries with NSNS and RR 3-form field strength fluxes. The flux parameters are controlled by the angles between the M5-brane and the (T)duality directions. For one M5-brane, the duality leads to a family of supersymmetric flux configurations which interpolates between imaginary self-dual fluxes and fluxes similar to the Polchinski-Strassler kind. For multiple M5-branes, the IIB configurations are related to fluxes for twisted sector fields in orbifolds. The dual M5-brane picture also provides a geometric interpretation for several properties of flux configurations (like the supersymmetry conditions, their contribution to tadpoles, etc), and for many non-trivial effects in the IIB side. Among the latter, the dielectric effect for probe D3-branes is dual to the recombination of probe M5-branes with background ones; also, a picture of a decay channel for non-supersymmetric fluxes is suggested.Comment: 30 pages, 3 figure

Nonsingular and accelerated expanding universe from effective Yang-Mills theory

The energy-momentum tensor coming from one-parameter effective Yang- Mills theory is here used to describe the matter-energy content of the homogeneous and isotropic Friedmann cosmology in its early stages. The behavior of all solutions is examined. Particularly, it is shown that only solutions corresponding to an open model allow the universe to evolve into an accelerated expansion. This result appears as a possible mechanism for an inflationary phase produced by a vector field. Further, depending on the value of some parameters characterizing the system, the resulting models are classified as singular or nonsingular.Comment: 15 pages, 7 figures, some discussions were simplified and new remarks were introduce

A Bisognano-Wichmann-like Theorem in a Certain Case of a Non Bifurcate Event Horizon related to an Extreme Reissner-Nordstr\"om Black Hole

Thermal Wightman functions of a massless scalar field are studied within the framework of a ``near horizon'' static background model of an extremal R-N black hole. This model is built up by using global Carter-like coordinates over an infinite set of Bertotti-Robinson submanifolds glued together. The analytical extendibility beyond the horizon is imposed as constraints on (thermal) Wightman's functions defined on a Bertotti-Robinson sub manifold. It turns out that only the Bertotti-Robinson vacuum state, i.e. $T=0$, satisfies the above requirement. Furthermore the extension of this state onto the whole manifold is proved to coincide exactly with the vacuum state in the global Carter-like coordinates. Hence a theorem similar to Bisognano-Wichmann theorem for the Minkowski space-time in terms of Wightman functions holds with vanishing ``Unruh-Rindler temperature''. Furtermore, the Carter-like vacuum restricted to a Bertotti-Robinson region, resulting a pure state there, has vanishing entropy despite of the presence of event horizons. Some comments on the real extreme R-N black hole are given

Beam instrumentation for the Tevatron Collider

The Tevatron in Collider Run II (2001-present) is operating with six times more bunches and many times higher beam intensities and luminosities than in Run I (1992-1995). Beam diagnostics were crucial for the machine start-up and the never-ending luminosity upgrade campaign. We present the overall picture of the Tevatron diagnostics development for Run II, outline machine needs for new instrumentation, present several notable examples that led to Tevatron performance improvements, and discuss the lessons for future colliders