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

Femtoscopy of the system shape fluctuations in heavy ion collisions

Dipole, triangular, and higher harmonic flow that have an origin in the initial density fluctuations has gained a lot of attention as they can provide additional important information about the dynamical properties (e.g. viscosity) of the system. The fluctuations in the initial geometry should be also reflected in the detail shape and velocity field of the system at freeze-out. In this talk I discuss the possibility to measure such fluctuations by means of identical and non-identical particle interferometry.Comment: 4 pages, Proceedings of Quark Matter 2011 Conference, May 23 - May 28, Annecy, Franc

Derivative corrections to the Born-Infeld action through beta-function calculations in N=2 boundary superspace

We calculate the beta-functions for an open string sigma-model in the presence of a U(1) background. Passing to N=2 boundary superspace, in which the background is fully characterized by a scalar potential, significantly facilitates the calculation. Performing the calculation through three loops yields the equations of motion up to five derivatives on the fieldstrengths, which upon integration gives the bosonic sector of the effective action for a single D-brane in trivial bulk background fields through four derivatives and to all orders in alpha'. Finally, the present calculation shows that demanding ultra-violet finiteness of the non-linear sigma-model can be reformulated as the requirement that the background is a deformed stable holomorphic U(1) bundle.Comment: 25 pages, numerous figure

Representations of the discrete inhomogeneous Lorentz group and Dirac wave equation on the lattice

We propose the fundamental and two dimensional representation of the Lorentz groups on a (3+1)-dimensional hypercubic lattice, from which representations of higher dimensions can be constructed. For the unitary representation of the discrete translation group we use the kernel of the Fourier transform. From the Dirac representation of the Lorentz group (including reflections) we derive in a natural way the wave equation on the lattice for spin 1/2 particles. Finally the induced representation of the discrete inhomogeneous Lorentz group is constructed by standard methods and its connection with the continuous case is discussed.Comment: LaTeX, 20 pages, 1 eps figure, uses iopconf.sty (late submission

Holographic Multiverse

We explore the idea that the dynamics of the inflationary multiverse is encoded in its future boundary, where it is described by a lower dimensional theory which is conformally invariant in the UV. We propose that a measure for the multiverse, which is needed in order to extract quantitative probabilistic predictions, can be derived in terms of the boundary theory by imposing a UV cutoff. In the inflationary bulk, this is closely related (though not identical) to the so-called scale factor cutoff measure.Comment: 23 pages, 4 figures. Replaced to match published versio

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

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

Casimir effect due to a single boundary as a manifestation of the Weyl problem

The Casimir self-energy of a boundary is ultraviolet-divergent. In many cases the divergences can be eliminated by methods such as zeta-function regularization or through physical arguments (ultraviolet transparency of the boundary would provide a cutoff). Using the example of a massless scalar field theory with a single Dirichlet boundary we explore the relationship between such approaches, with the goal of better understanding the origin of the divergences. We are guided by the insight due to Dowker and Kennedy (1978) and Deutsch and Candelas (1979), that the divergences represent measurable effects that can be interpreted with the aid of the theory of the asymptotic distribution of eigenvalues of the Laplacian discussed by Weyl. In many cases the Casimir self-energy is the sum of cutoff-dependent (Weyl) terms having geometrical origin, and an "intrinsic" term that is independent of the cutoff. The Weyl terms make a measurable contribution to the physical situation even when regularization methods succeed in isolating the intrinsic part. Regularization methods fail when the Weyl terms and intrinsic parts of the Casimir effect cannot be clearly separated. Specifically, we demonstrate that the Casimir self-energy of a smooth boundary in two dimensions is a sum of two Weyl terms (exhibiting quadratic and logarithmic cutoff dependence), a geometrical term that is independent of cutoff, and a non-geometrical intrinsic term. As by-products we resolve the puzzle of the divergent Casimir force on a ring and correct the sign of the coefficient of linear tension of the Dirichlet line predicted in earlier treatments.Comment: 13 pages, 1 figure, minor changes to the text, extra references added, version to be published in J. Phys.

Freak observers and the measure of the multiverse

I suggest that the factor $p_j$ in the pocket-based measure of the multiverse, $P_j=p_j f_j$, should be interpreted as accounting for equilibrium de Sitter vacuum fluctuations, while the selection factor $f_j$ accounts for the number of observers that were formed due to non-equilibrium processes resulting from such fluctuations. I show that this formulation does not suffer from the problem of freak observers (also known as Boltzmann brains).Comment: 6 pages, no figures; references adde

S3 x Z2 model for neutrino mass matrices

We propose a model for lepton mass matrices based on the seesaw mechanism, a complex scalar gauge singlet and a horizontal symmetry S_3 \times \mathbbm{Z}_2. In a suitable weak basis, the charged-lepton mass matrix and the neutrino Dirac mass matrix are diagonal, but the vacuum expectation value of the scalar gauge singlet renders the Majorana mass matrix of the right-handed neutrinos non-diagonal, thereby generating lepton mixing. When the symmetry $S_3$ is not broken in the scalar potential, the effective light-neutrino Majorana mass matrix enjoys $\mu$--$\tau$ interchange symmetry, thus predicting maximal atmospheric neutrino mixing together with $U_{e3} = 0$. A partial and less predictive form of $\mu$--$\tau$ interchange symmetry is obtained when the symmetry $S_3$ is softly broken in the scalar potential. Enlarging the symmetry group S_3 \times \mathbbm{Z}_2 by an additional discrete electron-number symmetry \mathbbm{Z}_2^{(e)}, a more predicitive model is obtained, which is in practice indistinguishable from a previous one based on the group $D_4$.Comment: 13 pages, 3 figures, final version for publication in JHE