Distances on a one-dimensional lattice from noncommutative geometry

In the following paper we continue the work of Bimonte-Lizzi-Sparano on distances on a one dimensional lattice. We succeed in proving analytically the exact formulae for such distances. We find that the distance to an even point on the lattice is the geometrical average of the ``predecessor'' and ``successor'' distances to the neighbouring odd points.Comment: LaTeX file, few minor typos corrected, 9 page

Generalized inversion of the Hochschild coboundary operator and deformation quantization

Using a derivative decomposition of the Hochschild differential complex we define a generalized inverse of the Hochschild coboundary operator. It can be applied for systematic computations of star products on Poisson manifolds.Comment: 9 pages, misprints correcte

Absence of epidemic threshold in scale-free networks with connectivity correlations

Random scale-free networks have the peculiar property of being prone to the spreading of infections. Here we provide an exact result showing that a scale-free connectivity distribution with diverging second moment is a sufficient condition to have null epidemic threshold in unstructured networks with either assortative or dissortative mixing. Connectivity correlations result therefore ininfluential for the epidemic spreading picture in these scale-free networks. The present result is related to the divergence of the average nearest neighbors connectivity, enforced by the connectivity detailed balance condition

Spectral theorem for the Lindblad equation for quadratic open fermionic systems

The spectral theorem is proven for the quantum dynamics of quadratic open systems of n fermions described by the Lindblad equation. Invariant eigenspaces of the many-body Liouvillean dynamics and their largest Jordan blocks are explicitly constructed for all eigenvalues. For eigenvalue zero we describe an algebraic procedure for constructing (possibly higher dimensional) spaces of (degenerate) non-equilibrium steady states.Comment: 19 pages, no figure

Entropy Rate of Diffusion Processes on Complex Networks

The concept of entropy rate for a dynamical process on a graph is introduced. We study diffusion processes where the node degrees are used as a local information by the random walkers. We describe analitically and numerically how the degree heterogeneity and correlations affect the diffusion entropy rate. In addition, the entropy rate is used to characterize complex networks from the real world. Our results point out how to design optimal diffusion processes that maximize the entropy for a given network structure, providing a new theoretical tool with applications to social, technological and communication networks.Comment: 4 pages (APS format), 3 figures, 1 tabl

Heat operator with pure soliton potential: properties of Jost and dual Jost solutions

Properties of Jost and dual Jost solutions of the heat equation, $\Phi(x,k)$ and $\Psi(x,k)$, in the case of a pure solitonic potential are studied in detail. We describe their analytical properties on the spectral parameter $k$ and their asymptotic behavior on the $x$-plane and we show that the values of $e^{-qx}\Phi(x,k)$ and the residua of $e^{qx}\Psi(x,k)$ at special discrete values of $k$ are bounded functions of $x$ in a polygonal region of the $q$-plane. Correspondingly, we deduce that the extended version $L(q)$ of the heat operator with a pure solitonic potential has left and right annihilators for $q$ belonging to these polygonal regions.Comment: 26 pages, 3 figure

Majorana spinors and extended Lorentz symmetry in four-dimensional theory

An extended local Lorentz symmetry in four-dimensional (4D) theory is considered. A source of this symmetry is a group of general linear transformations of four-component Majorana spinors GL(4,M) which is isomorphic to GL(4,R) and is the covering of an extended Lorentz group in a 6D Minkowski space M(3,3) including superluminal and scaling transformations. Physical space-time is assumed to be a 4D pseudo-Riemannian manifold. To connect the extended Lorentz symmetry in the M(3,3) space with the physical space-time, a fiber bundle over the 4D manifold is introduced with M(3,3) as a typical fiber. The action is constructed which is invariant with respect to both general 4D coordinate and local GL(4,M) spinor transformations. The components of the metric on the 6D fiber are expressed in terms of the 4D pseudo-Riemannian metric and two extra complex fields: 4D vector and scalar ones. These extra fields describe in the general case massive particles interacting with an extra U(1) gauge field and weakly interacting with ordinary particles, i.e. possessing properties of invisible (dark) matter.Comment: 24 page

Symmetric extendibility for qudits and tolerable error rates in quantum cryptography

Symmetric extendibility of quantum states has recently drawn attention in the context of quantum cryptography to judge whether quantum states shared between two distant parties can be purified by means of one-way error correction protocols. In this letter we study the symmetric extendibility in a specific class of two-qudit states, i. e. states composed of two d-level systems, in order to find upper bounds on tolerable error rates for a wide class of qudit-based quantum cryptographic protocols using two-way error correction. In important cases these bounds coincide with previously known lower bounds, thereby proving sharpness of these bounds in arbitrary finite-dimensional systems.Comment: 4 pages, no figure

Soliton solutions of the Kadomtsev-Petviashvili II equation

We study a general class of line-soliton solutions of the Kadomtsev-Petviashvili II (KPII) equation by investigating the Wronskian form of its tau-function. We show that, in addition to previously known line-soliton solutions, this class also contains a large variety of new multi-soliton solutions, many of which exhibit nontrivial spatial interaction patterns. We also show that, in general, such solutions consist of unequal numbers of incoming and outgoing line solitons. From the asymptotic analysis of the tau-function, we explicitly characterize the incoming and outgoing line-solitons of this class of solutions. We illustrate these results by discussing several examples.Comment: 28 pages, 4 figure

Quantum wire junctions breaking time reversal invariance

We explore the possibility to break time reversal invariance at the junction of quantum wires. The universal features in the bulk of the wires are described by the anyon Luttinger liquid. A simple necessary and sufficient condition for the breaking of time reversal invariance is formulated in terms of the scattering matrix at the junction. The phase diagram of a junction with generic number of wires is investigated in this framework. We give an explicit classification of those critical points which can be reached by bosonization and study the interplay between their stability and symmetry content.Comment: Extended version (Appendices C and D and some references added, typos corrected) to appear in Phys. Rev.