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

Giant acceleration in slow-fast space-periodic Hamiltonian systems

Motion of an ensemble of particles in a space-periodic potential well with a weak wave-like perturbation imposed is considered. We found that slow oscillations of wavenumber of the perturbation lead to occurrence of directed particle current. This current is amplifying with time due to giant acceleration of some particles. It is shown that giant acceleration is linked with the existence of resonant channels in phase space

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

Canonical Representatives of Morphic Permutations

An infinite permutation can be defined as a linear ordering of the set of natural numbers. In particular, an infinite permutation can be constructed with an aperiodic infinite word over $\{0,\ldots,q-1\}$ as the lexicographic order of the shifts of the word. In this paper, we discuss the question if an infinite permutation defined this way admits a canonical representative, that is, can be defined by a sequence of numbers from [0, 1], such that the frequency of its elements in any interval is equal to the length of that interval. We show that a canonical representative exists if and only if the word is uniquely ergodic, and that is why we use the term ergodic permutations. We also discuss ways to construct the canonical representative of a permutation defined by a morphic word and generalize the construction of Makarov, 2009, for the Thue-Morse permutation to a wider class of infinite words.Comment: Springer. WORDS 2015, Sep 2015, Kiel, Germany. Combinatorics on Words: 10th International Conference. arXiv admin note: text overlap with arXiv:1503.0618

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

Calculating loops without loop calculations: NLO computation of pentaquark correlators

We compute next-to-leading order (NLO) perturbative QCD corrections to the correlators of interpolating pentaquark currents. We employ modular techniques in configuration space which saves us from the onus of having to do loop calculations. The modular technique is explained in some detail. We present explicit NLO results for several interpolating pentaquark currents that have been written down in the literature. Our modular approach is easily adapted to the case of NLO corrections to multiquark correlators with an arbitrary number of quarks/antiquarks.Comment: 23 pages, 1 figure, published version. arXiv admin note: text overlap with arXiv:hep-lat/031001

Duality in multi-channel Luttinger Liquid with local scatterer

We have devised a general scheme that reveals multiple duality relations valid for all multi-channel Luttinger Liquids. The relations are universal and should be used for establishing phase diagrams and searching for new non-trivial phases in low-dimensional strongly correlated systems. The technique developed provides universal correspondence between scaling dimensions of local perturbations in different phases. These multiple relations between scaling dimensions lead to a connection between different inter-phase boundaries on the phase diagram. The dualities, in particular, constrain phase diagram and allow predictions of emergence and observation of new phases without explicit model-dependent calculations. As an example, we demonstrate the impossibility of non-trivial phase existence for fermions coupled to phonons in one dimension