Level-spacing distribution of a fractal matrix

We diagonalize numerically a Fibonacci matrix with fractal Hilbert space structure of dimension $d_{f}=1.8316...$ We show that the density of states is logarithmically normal while the corresponding level-statistics can be described as critical since the nearest-neighbor distribution function approaches the intermediate semi-Poisson curve. We find that the eigenvector amplitudes of this matrix are also critical lying between extended and localized.Comment: 6 pages, Latex file, 4 postscript files, published in Phys. Lett. A289 pp 183-7 (2001

First passage time exponent for higher-order random walks:Using Levy flights

We present a heuristic derivation of the first passage time exponent for the integral of a random walk [Y. G. Sinai, Theor. Math. Phys. {\bf 90}, 219 (1992)]. Building on this derivation, we construct an estimation scheme to understand the first passage time exponent for the integral of the integral of a random walk, which is numerically observed to be $0.220\pm0.001$. We discuss the implications of this estimation scheme for the $n{\rm th}$ integral of a random walk. For completeness, we also address the $n=\infty$ case. Finally, we explore an application of these processes to an extended, elastic object being pulled through a random potential by a uniform applied force. In so doing, we demonstrate a time reparameterization freedom in the Langevin equation that maps nonlinear stochastic processes into linear ones.Comment: 4 figures, submitted to PR

Extended electronic states in disordered 1-d lattices: an example

We discuss a very simple model of a 1-d disordered lattice, in which {\em all} the electronic eigenstates are extended. The nature of these states is examined from several viewpoints, and it is found that the eigenfunctions are not Bloch functions although they extend throughout the chain. Some typical wavefunctions are plotted. This problem originated in our earlier study of extended states in the quasiperiodic copper-mean lattice [ Sil, Karmakar, Moitra and Chakrabarti, Phys. Rev. B (1993) ]. In the present investigation extended states are found to arise from a different kind of correlation than that of the well-known dimer-type.Comment: 9 pages, 1 figure available on request, LaTex version 2.09, SINP-SSMP93-0

Effective action approach and Carlson-Goldman mode in d-wave superconductors

We theoretically investigate the Carlson-Goldman (CG) mode in two-dimensional clean d-wave superconductors using the effective ``phase only'' action formalism. In conventional s-wave superconductors, it is known that the CG mode is observed as a peak in the structure factor of the pair susceptibility $S(\Omega, \mathbf{K})$ only just below the transition temperature T_c and only in dirty systems. On the other hand, our analytical results support the statement by Y.Ohashi and S.Takada, Phys.Rev.B {\bf 62}, 5971 (2000) that in d-wave superconductors the CG mode can exist in clean systems down to the much lower temperatures, $T \approx 0.1 T_c$. We also consider the manifestations of the CG mode in the density-density and current-current correlators and discuss the gauge independence of the obtained results.Comment: 23 pages, RevTeX4, 12 EPS figures; final version to appear in PR

One-Dimensional Extended States in Partially Disordered Planar Systems

We obtain analytically a continuum of one-dimensional ballistic extended states in a two-dimensional disordered system, which consists of compactly coupled random and pure square lattices. The extended states give a marginal metallic phase with finite conductivity $\sigma_{0}=2e^2/h$ in a wide energy range, whose boundaries define the mobility edges of a first-order metal-insulator transition. We show current-voltage duality, $H_{\parallel}/T$ scaling of the conductivity in parallel magnetic field $H_{\parallel}$ and non-Fermi liquid properties when long-range electron-electron interactions are included.Comment: 4 pages, revtex file, 3 postscript file

Quantum backreaction of massive fields and self-consistent semiclassical extreme black holes and acceleration horizons

We consider the effect of backreaction of quantized massive fields on the metric of extreme black holes (EBH). We find the analytical approximate expression for the stress-energy tensor for a scalar (with an arbitrary coupling), spinor and vector fields near an event horizon. We show that, independent of a concrete type of EBH, the energy measured by a freely falling observer is finite on the horizon, so that quantum backreaction is consistent with the existence of EBH. For the Reissner-Nordstrom EBH with a total mass M_{tot} and charge Q we show that for all cases of physical interest M_{tot}< Q. We also discuss different types of quantum-corrected Bertotti-Robinson spacetimes, find for them exact self-consistent solutions and consider situations in which tiny quantum corrections lead to the qualitative change of the classical geometry and topology. In all cases one should start not from a classical background with further adding quantum corrections but from the quantum-corrected self-consistent geometries from the very beginning.Comment: Minor corrections. To appear in Phys. Rev.

Anomalous tag diffusion in the asymmetric exclusion model with particles of arbitrary sizes

Anomalous behavior of correlation functions of tagged particles are studied in generalizations of the one dimensional asymmetric exclusion problem. In these generalized models the range of the hard-core interactions are changed and the restriction of relative ordering of the particles is partially brocken. The models probing these effects are those of biased diffusion of particles having size S=0,1,2,..., or an effective negative "size" S=-1,-2,..., in units of lattice space. Our numerical simulations show that irrespective of the range of the hard-core potential, as long some relative ordering of particles are kept, we find suitable sliding-tag correlation functions whose fluctuations growth with time anomalously slow ($t^{{1/3}}$), when compared with the normal diffusive behavior ($t^{{1/2}}$). These results indicate that the critical behavior of these stochastic models are in the Kardar-Parisi-Zhang (KPZ) universality class. Moreover a previous Bethe-ansatz calculation of the dynamical critical exponent $z$, for size $S \geq 0$ particles is extended to the case $S<0$ and the KPZ result $z=3/2$ is predicted for all values of $S \in {Z}$.Comment: 4 pages, 3 figure

Statistical and Dynamical Study of Disease Propagation in a Small World Network

We study numerically statistical properties and dynamical disease propagation using a percolation model on a one dimensional small world network. The parameters chosen correspond to a realistic network of school age children. We found that percolation threshold decreases as a power law as the short cut fluctuations increase. We found also the number of infected sites grows exponentially with time and its rate depends logarithmically on the density of susceptibles. This behavior provides an interesting way to estimate the serology for a given population from the measurement of the disease growing rate during an epidemic phase. We have also examined the case in which the infection probability of nearest neighbors is different from that of short cuts. We found a double diffusion behavior with a slower diffusion between the characteristic times.Comment: 12 pages LaTex, 10 eps figures, Phys.Rev.E Vol. 64, 056115 (2001

Interplay of spin density wave and superconductivity with different pairing symmetry

A model study for the coexistence of the spin density wave and superconductivity is presented. With reference to the recent angle resolved photo emmission experimental data in high T_c cuprates, presence of the nested pieces of bands is assumed. The single band Hubbard model, therefore, when treated within the Hatree-Fock mean field theory leads to a spin density wave (SDW) ground state. The superconductivity (SC) is assumed to be due to a generalised attractive potential with a separable form without specifying to any particular origin. It therefore allows a comparative study of the coexistence of superconductivity of different order parameter symmetry with the spin density wave state. We find that the phase diagram, comprising of the amplitudes of the respective gaps (SC and SDW) Vs. band filling resembles to that of the high T_c cuprates only when the order parameter of the superconducting phase has d-wave symmetry. Thermal variation of different order parameters (e.g, SC and SDW) also show interesting coexistence and reentrance behaviors that are consistent with experimental observations, specially for the borocarbides.Comment: 8 pages, 6 figures (postscript attached), Physica C (in press

Transverse optical Josephson plasmons, equations of motion

A detailed calculation is presented of the dielectric function in superconducttors consisting of two Josephson coupled superconducting layers per unit cell, taking into account the effect of finite compressibility of the electron fluid. From the model it follows, that two longitudinal, and one transverse optical Josephson plasma resonance exist in these materials, for electric field polarization perpendicular to the planes. The latter mode appears as a resonance in the transverse dielectric function, and it couples directly to the electrical field vector of infrared radiation. A shift of all plasma frequencies, and a reduction of the intensity of the transverse optical Josephson plasmon is shown to result from the finite compressibility of the electron fluid.Comment: 17 pages, ReVTeX, 7 figures in eps forma