Two-dimensional algebro-geometric difference operators

A generalized inverse problem for a two-dimensional difference operator is introduced. A new construction of the algebro-geometric difference operators of two types first considered by I.M.Krichever and S.P.Novikov is proposedComment: 11 pages; added references, enlarged introduction, rewritten abstrac

Distribution of averages in a correlated Gaussian medium as a tool for the estimation of the cluster distribution on size

Calculation of the distribution of the average value of a Gaussian random field in a finite domain is carried out for different cases. The results of the calculation demonstrate a strong dependence of the width of the distribution on the spatial correlations of the field. Comparison with the simulation results for the distribution of the size of the cluster indicates that the distribution of an average field could serve as a useful tool for the estimation of the asymptotic behavior of the distribution of the size of the clusters for "deep" clusters where value of the field on each site is much greater than the rms disorder.Comment: 15 pages, 6 figures, RevTe

Topological Phenomena in the Real Periodic Sine-Gordon Theory

The set of real finite-gap Sine-Gordon solutions corresponding to a fixed spectral curve consists of several connected components. A simple explicit description of these components obtained by the authors recently is used to study the consequences of this property. In particular this description allows to calculate the topological charge of solutions (the averaging of the $x$-derivative of the potential) and to show that the averaging of other standard conservation laws is the same for all components.Comment: LaTeX, 18 pages, 3 figure

WZW action in odd dimensional gauge theories

It is shown that Wess-Zumino-Witten (WZW) type actions can be constructed in odd dimensional space-times using Wilson line or Wilson loop. WZW action constructed using Wilson line gives anomalous gauge variations and the WZW action constructed using Wilson loop gives anomalous chiral transformation. We show that pure gauge theory including Yang-Mills action, Chern-Simons action and the WZW action can be defined in odd dimensional space-times with even dimensional boundaries. Examples in 3D and 5D are given. We emphasize that this offers a way to generalize gauge theory in odd dimensions. The WZW action constructed using Wilson line can not be considered as action localized on boundary space-times since it can give anomalous gauge transformations on separated boundaries. We try to show that such WZW action can be obtained in the effective theory when making localized chiral fermions decouple.Comment: 19 pages, text shortened, reference added. Version to appear in PR

Oscillation of linear ordinary differential equations: on a theorem by A. Grigoriev

We give a simplified proof and an improvement of a recent theorem by A. Grigoriev, placing an upper bound for the number of roots of linear combinations of solutions to systems of linear equations with polynomial or rational coefficients.Comment: 16 page

Temperature-dependent Drude transport in a two-dimensional electron gas

We consider transport of dilute two-dimensional electrons, with temperature between Fermi and Debye temperatures. In this regime, electrons form a nondegenerate plasma with mobility limited by potential disorder. Different kinds of impurities contribute unique signatures to the resulting temperature-dependent Drude conductivity, via energy-dependent scattering. This opens up a way to characterize sample disorder composition. In particular, neutral impurities cause a slow decrease in conductivity with temperature, whereas charged impurities result in conductivity growing as a square root of temperature. This observation serves as a precaution for literally interpreting metallic or insulating conductivity dependence, as both can be found in a classical metallic system.Comment: 5 pages, 2 figures, published versio