Signum Function Method for Generation of Correlated Dichotomic Chains

We analyze the signum-generation method for creating random dichotomic sequences with prescribed correlation properties. The method is based on a binary mapping of the convolution of continuous random numbers with some function originated from the Fourier transform of a binary correlator. The goal of our study is to reveal conditions under which one can construct binary sequences with a given pair correlator. Our results can be used in the construction of superlattices and waveguides with selective transport properties.Comment: 14 pages, 7 figure

Onset of Delocalization in Quasi-1D Waveguides with Correlated Surface Disorder

We present first analytical results on transport properties of many-mode waveguides with rough surfaces having long-range correlations. We show that propagation of waves through such waveguides reveals a quite unexpected phenomena of a complete transparency for a subset of propagating modes. These modes do not interact with each other and effectively can be described by the theory of 1D transport with correlated disorder. We also found that with a proper choice of model parameters one can arrange a perfect transparency of waveguides inside a given window of energy of incoming waves. The results may be important in view of experimental realizations of a selective transport in application to both waveguides and electron/optic nanodevices.Comment: RevTex, 4 pages, no figures, few references are adde

The Threshold effects for the two-particle Hamiltonians on lattices

For a wide class of two-body energy operators $h(k)$ on the three-dimensional lattice \bbZ^3, $k$ being the two-particle quasi-momentum, we prove that if the following two assumptions (i) and (ii) are satisfied, then for all nontrivial values $k$, $k\ne 0$, the discrete spectrum of $h(k)$ below its threshold is non-empty. The assumptions are: (i) the two-particle Hamiltonian $h(0)$ corresponding to the zero value of the quasi-momentum has either an eigenvalue or a virtual level at the bottom of its essential spectrum and (ii) the one-particle free Hamiltonians in the coordinate representation generate positivity preserving semi-groups

Non-perturbative results for the spectrum of surface-disordered waveguides

We calculated the spectrum of normal scalar waves in a planar waveguide with absolutely soft randomly rough boundaries beyond the perturbation theories in the roughness heights and slopes, basing on the exact boundary scattering potential. The spectrum is proved to be a nearly real non-analytic function of the dispersion $\zeta^2$ of the roughness heights (with square-root singularity) as $\zeta^2 \to 0$. The opposite case of large boundary defects is summarized.Comment: REVTEX 3, OSA style, 9 pages, no figures. Submitted to Optics Letter