Fluctuation-induced traffic congestion in heterogeneous networks

In studies of complex heterogeneous networks, particularly of the Internet, significant attention was paid to analyzing network failures caused by hardware faults or overload, where the network reaction was modeled as rerouting of traffic away from failed or congested elements. Here we model another type of the network reaction to congestion -- a sharp reduction of the input traffic rate through congested routes which occurs on much shorter time scales. We consider the onset of congestion in the Internet where local mismatch between demand and capacity results in traffic losses and show that it can be described as a phase transition characterized by strong non-Gaussian loss fluctuations at a mesoscopic time scale. The fluctuations, caused by noise in input traffic, are exacerbated by the heterogeneous nature of the network manifested in a scale-free load distribution. They result in the network strongly overreacting to the first signs of congestion by significantly reducing input traffic along the communication paths where congestion is utterly negligible.Comment: 4 pages, 3 figure

Tunnelling density of states at Coulomb blockade peaks

We calculate the tunnelling density of states (TDoS) for a quantum dot in the Coulomb blockade regime, using a functional integral representation with allowing correctly for the charge quantisation. We show that in addition to the well-known gap in the TDoS in the Coulomb-blockade valleys, there is a suppression of the TDoS at the peaks. We show that such a suppression is necessary in order to get the correct result for the peak of the differential conductance through an almost close quantum dot.Comment: 6 pages, 2 figure

Quasi-localized states in disordered metals and non-analyticity of the level curvature distribution function

It is shown that the quasi-localized states in weakly disordered systems can lead to the non-analytical distribution of level curvatures. In 2D systems the distribution function P(K) has a branching point at K=0. In quasi-1D systems the non-analyticity at K=0 is very weak, and in 3D metals it is absent at all. Such a behavior confirms the conjecture that the branching at K=0 is due to the multi-fractality of wave functions and thus is a generic feature of all critical eigenstates. The relationsip between the branching power and the multi-fractality exponent $\eta(2)$ is derived.Comment: 4 pages, LATE

Functional Integral Bosonization for Impurity in Luttinger Liquid

We use a functional integral formalism developed earlier for the pure Luttinger liquid (LL) to find an exact representation for the electron Green function of the LL in the presence of a single backscattering impurity. This allows us to reproduce results (well known from the bosonization techniques) for the suppression of the electron local density of states (LDoS) at the position of the impurity and for the Friedel oscillations at finite temperature. In addition, we have extracted from the exact representation an analytic dependence of LDoS on the distance from the impurity and shown how it crosses over to that for the pure LL.Comment: 7 pages, 1 LaTeX produced figur

An inhomogeneous Josephson phase in thin-film and High-Tc superconductors

In many cases inhomogeneities are known to exist near the metal (or superconductor)-insulator transition, as follows from well-known domain-wall arguments. If the conducting regions are large enough (i.e. when the T=0 superconducting gap is much larger than the single-electron level spacing), and if they have superconducting correlations, it becomes energetically favorable for the system to go into a Josephson-coupled zero-resistance state before (i.e. at higher resistance than) becoming a "real" metal. We show that this is plausible by a simple comparison of the relevant coupling constants. For small grains in the above sense, the electronic grain structure is washed out by delocalization and thus becomes irrelevant. When the proposed "Josephson state" is quenched by a magnetic field, an insulating, rather then a metallic, state should appear. This has been shown to be consistent with the existing data on oxide materials as well as ultra-thin films. We discuss the Uemura correlations versus the Homes law, and derive the former for the large-grain Josephson array (inhomogenous superconductor) model. The small-grain case behaves like a dirty homogenous metal. It should obey the Homes law provided that the system is in the dirty supeconductivity limit. A speculation why that is typically the case for d-wave superconductors is presented.Comment: Conference proceeding for "Fluctuations in Superconductors" held in Nazareth, Israel in June, 2007; 6 pages with 1 figure, to appear in Physica

Level Curvature Distribution and the Structure of Eigenfunctions in Disordered Systems

The level curvature distribution function is studied both analytically and numerically for the case of T-breaking perturbations over the orthogonal ensemble. The leading correction to the shape of the curvature distribution beyond the random matrix theory is calculated using the nonlinear supersymmetric sigma-model and compared to numerical simulations on the Anderson model. It is predicted analytically and confirmed numerically that the sign of the correction is different for T-breaking perturbations caused by a constant vector-potential equivalent to a phase twist in the boundary conditions, and those caused by a random magnetic field. In the former case it is shown using a nonperturbative approach that quasi-localized states in weakly disordered systems can cause the curvature distribution to be nonanalytic. In $2d$ systems the distribution function $P(K)$ has a branching point at K=0 that is related to the multifractality of the wave functions and thus should be a generic feature of all critical eigenstates. A relationship between the branching power and the multifractality exponent $d_{2}$ is suggested. Evidence of the branch-cut singularity is found in numerical simulations in $2d$ systems and at the Anderson transition point in $3d$ systems.Comment: 34 pages (RevTeX), 8 figures (postscript

Non-universal corrections to the level curvature distribution beyond random matrix theory

The level curvature distribution function is studied beyond the random matrix theory for the case of T-breaking perturbations over the orthogonal ensemble. The leading correction to the shape of the level curvature distribution is calculated using the nonlinear sigma-model. The sign of the correction depends on the presence or absence of the global gauge invariance and is different for perturbations caused by the constant vector-potential and by the random magnetic field. Scaling arguments are discussed that indicate on the qualitative difference in the level statistics in the dirty metal phase for space dimensionalities $d4$.Comment: 4 pages, Late

Topological universality of level dynamics in quasi-one-dimensional disordered conductors

Nonperturbative, in inverse Thouless conductance 1/g, corrections to distributions of level velocities and level curvatures in quasi-one-dimensional disordered conductors with a topology of a ring subject to a constant vector potential are studied within the framework of the instanton approximation of nonlinear sigma-model. It is demonstrated that a global character of the perturbation reveals the universal features of the level dynamics. The universality shows up in the form of weak topological oscillations of the magnitude ~ exp(-g) covering the main bodies of the densities of level velocities and level curvatures. The period of discovered universal oscillations does not depend on microscopic parameters of conductor, and is only determined by the global symmetries of the Hamiltonian before and after the perturbation was applied. We predict the period of topological oscillations to be 4/(pi)^2 for the distribution function of level curvatures in orthogonal symmetry class, and 3^(1/2)/(pi) for the distribution of level velocities in unitary and symplectic symmetry classes.Comment: 15 pages (revtex), 3 figure

Topological phase transition in superconductors with mirror symmetry

We provide analytical and numerical evidence that the attractive two-dimensional Kitaev model on a lattice with mirror symmetry demonstrates an unusual 'intrinsic' phase at half filling. This phase emerges in the phase diagram at the boundary separating two topological superconductors with opposite Chern numbers and exists due to the condensation of non-zero momentum Cooper pairs. Unlike Fulde-Ferrell-Larkin-Ovchinnikov superconductivity, the Cooper pairs momenta are lying along two lines in the Brillouin zone meaning simultaneous condensation of a continuum of Cooper pairs

Optimal Fluctuations and Tail States of non-Hermitian Operators

We develop a general variational approach to study the statistical properties of the tail states of a wide class of non-Hermitian operators. The utility of the method, which is a refinement of the instanton approach introduced by Zittartz and Langer, is illustrated in detail by reference to the problem of a quantum particle propagating in an imaginary scalar potential.Comment: 4 pages, 2 figures, to appear in PR