Vlasov scaling for the Glauber dynamics in continuum

We consider Vlasov-type scaling for the Glauber dynamics in continuum with a positive integrable potential, and construct rescaled and limiting evolutions of correlation functions. Convergence to the limiting evolution for the positive density system in infinite volume is shown. Chaos preservation property of this evolution gives a possibility to derive a non-linear Vlasov-type equation for the particle density of the limiting system.Comment: 32 page

Extinction threshold in the spatial stochastic logistic model: space homogeneous case

We consider the extinction regime in the spatial stochastic logistic model in R^d (a.k.a. Bolker–Pacala–Dieckmann–Law model of spatial populations) using the first-order perturbation beyond the mean-field equation. In space homogeneous case (i.e. when the density is non-spatial and the covariance is translation invariant), we show that the perturbation converges as time tends to infinity; that yields the first-order approximation for the stationary density. Next, we study the critical mortality – the smallest constant death rate which ensures the extinction of the population – as a function of the mean-field scaling parameter ε>0. We find the leading term of the asymptotic expansion (as ε→0) of the critical mortality which is apparently different for the cases d≥3, d = 2, and d = 1

Vlasov scaling for stochastic dynamics of continuous systems

We describe a general scheme of derivation of the Vlasov-type equations for Markov evolutions of particle systems in continuum. This scheme is based on a proper scaling of corresponding Markov generators and has an algorithmic realization in terms of related hierarchical chains of correlation functions equations. Several examples of the realization of the proposed approach in particular models are presented.Comment: 23 page

On a conjecture of A. Magnus concerning the asymptotic behavior of the recurrence coefficients of the generalized Jacobi polynomials

In 1995 Magnus posed a conjecture about the asymptotics of the recurrence coefficients of orthogonal polynomials with respect to the weights on [-1,1] of the form $$(1-x)^\alpha (1+x)^\beta |x_0 - x|^\gamma \times a jump at x_0,$$ with $\alpha, \beta, \gamma>-1$ and $x_0 \in (-1,1)$. We show rigorously that Magnus' conjecture is correct even in a more general situation, when the weight above has an extra factor, which is analytic in a neighborhood of [-1,1] and positive on the interval. The proof is based on the steepest descendent method of Deift and Zhou applied to the non-commutative Riemann-Hilbert problem characterizing the orthogonal polynomials. A feature of this situation is that the local analysis at $x_0$ has to be carried out in terms of confluent hypergeometric functions.Comment: 29 pages, 4 figure

Compensation driven superconductor-insulator transition

The superconductor-insulator transition in the presence of strong compensation of dopants was recently realized in La doped YBCO. The compensation of acceptors by donors makes it possible to change independently the concentration of holes n and the total concentration of charged impurities N. We propose a theory of the superconductor-insulator phase diagram in the (N,n) plane. It exhibits interesting new features in the case of strong coupling superconductivity, where Cooper pairs are compact, non-overlapping bosons. For compact Cooper pairs the transition occurs at a significantly higher density than in the case of spatially overlapping pairs. We establish the superconductor-insulator phase diagram by studying how the potential of randomly positioned charged impurities is screened by holes or by strongly bound Cooper pairs, both in isotropic and layered superconductors. In the resulting self-consistent potential the carriers are either delocalized or localized, which corresponds to the superconducting or insulating phase, respectively

Two-eigenfunction correlation in a multifractal metal and insulator

We consider the correlation of two single-particle probability densities $|\Psi_{E}({\bf r})|^{2}$ at coinciding points ${\bf r}$ as a function of the energy separation $\omega=|E-E'|$ for disordered tight-binding lattice models (the Anderson models) and certain random matrix ensembles. We focus on the models in the parameter range where they are close but not exactly at the Anderson localization transition. We show that even far away from the critical point the eigenfunction correlation show the remnant of multifractality which is characteristic of the critical states. By a combination of the numerical results on the Anderson model and analytical and numerical results for the relevant random matrix theories we were able to identify the Gaussian random matrix ensembles that describe the multifractal features in the metal and insulator phases. In particular those random matrix ensembles describe new phenomena of eigenfunction correlation we discovered from simulations on the Anderson model. These are the eigenfunction mutual avoiding at large energy separations and the logarithmic enhancement of eigenfunction correlations at small energy separations in the two-dimensional (2D) and the three-dimensional (3D) Anderson insulator. For both phenomena a simple and general physical picture is suggested.Comment: 16 pages, 18 figure

РЕВЕНКО АНАТОЛИЙ ГРИГОРЬЕВИЧ. К 75-летию со дня рождения

The current article is dedicated to the 75th birthday anniversary of A.G. Revenko who is a famous specialist in the field of X-ray fluorescence analysis. His biographical data and the main career stages are presented. The list of references contains some of his scientific works. A.G. Revenko was born on October 24, 1944 at the Sosyka-I station of the Pavlovsky district of the Krasnodar Territory. In 1965, he graduated from the Physics Department of Rostov-on-Don State University and began to work at the Institute of Geochemistry of the Siberian Branch of the USSR Academy of Sciences (Irkutsk). In 1971, he defended his thesis on the topic of “Research and selection of the conditions of X-ray fluorescence determination of elements with small atomic numbers”. In 1971, A.G. Revenko began to work at the Institute of Applied Physics at Irkutsk State University. In 1977-1988, he was the head of the "Tsvetmetavtomatika" Irkutsk basic research laboratory of X-ray spectral analysis focused on the implementation of the method and the creation of automated analytical control systems at non-ferrous metallurgy enterprises. Since 1988, he has been working at the Institute of the Earth's Crust, SB RAS. Under his leadership and with his direct participation, dozens of X-ray fluorescence analysis techniques have been developed for a variety of environmental materials and industrial products (metals, non-ferrous metal ores, rocks, soils, materials of plant origin, etc.). His studies were described in of the monograph and doctoral dissertation on the topic of “X-ray spectral fluorescence analysis of natural materials”. Teaching activities of A.G. Revenko were at Irkutsk State University, Irkutsk State University of Railway Engineering and Mongolian State University. A.G. Revenko was awarded the “Eson Erdene” Medal for his outstanding contribution to the training of Mongolian specialists. He is the author and co-author of more than 350 publications in journals, conference proceedings and other publications and has four copyright certificates for the inventions. He also served as a scientific adviser for 6 candidates of sciences.Keywords: X-ray fluorescence analysis of natural materials(Russian)А.L. Finkelshtein1, G.V. Pashkova21Vinogradov Institute of Geochemistry, SB RAS, Favorsky st., 1A, Irkutsk,664033, Russian Federation2Institute of the Earth’s Crust,SB RAS, Lermontov st., 128, Irkutsk, 664033, Russian FederationСтатья посвящена 75-летию известного специалиста в области рентгеноспектрального флуоресцентного анализа А.Г. Ревенко. Представлены основные биографические данные, этапы творческого пути, в списке литературы приведены некоторые из его многочисленных научных работ.А.Г. Ревенко родился 24 октября 1944 г. на станции Сосыка-I Павловского района Краснодарского края. В 1965 г. окончил физический факультет Ростовского-на-Дону госуниверситета. После окончания университета поступил на работу, а затем и в аспирантуру Института геохимии СО АН СССР (г. Иркутск). В 1971 г. защитил кандидатскую диссертацию на тему «Исследование и выбор условий РФА элементов с малыми атомными номерами». В 1971 г. А.Г. Ревенко переходит на работу в Институт прикладной физики при Иркутском госуниверситете. В 1977–1988 гг. возглавлял Иркутскую базовую научно-исследовательскую лабораторию рентгеноспектрального анализа “Цветметавтоматика”, ориентированную на внедрение метода и создание автоматизированных систем аналитического контроля на предприятиях цветной металлургии. С 1988 г. работает в Институте земной коры СО РАН. Под его руководством и при его непосредственном участии разработаны десятки методик рентгенофлуресцентного анализа разнообразных природных сред и промышленных продуктов (металлы, руды цветных металлов, горные породы, почвы, материалы растительного происхождения, и др.). Эти его исследования легли в основу монографии и докторской диссертации на тему “Рентгеноспектральный флуоресцентный анализ природных материалов”. Преподавательская деятельность А.Г. Ревенко проходила в Иркутском госуниверситете, Иркутском государственном университете путей сообщения и Монгольском государственном университете. За выдающийся вклад в подготовку монгольских специалистов А.Г. Ревенко награждён медалью «Есон Эрдэнэ». Он автор и соавтор более 350 публикаций в журналах, материалах конференций и др. изданиях, четырех авторских свидетельств на изобретение, подготовил 6 кандидатов наук.Ключевые слова: рентгенофлуоресцентный анализ природных материало

"Unusual" metals in two dimensions: one-particle model of the metal-insulator transition at T=0

The conductance of disordered nano-wires at T=0 is calculated in one-particle approximation by reducing the original multi-dimensional problem for an open bounded system to a set of exactly one-dimensional non-Hermitian problems for mode propagators. Regarding two-dimensional conductor as a limiting case of three-dimensional disordered quantum waveguide, the metallic ground state is shown to result from its multi-modeness. On thinning the waveguide (in practice, e. g., by means of the ``pressing'' external electric field) the electron system undergoes a continuous phase transition from metallic to insulating state. The result predicted conform qualitatively to the observed anomalies of the resistance of different planar electron and hole systems.Comment: 7 pages, LATEX-2

Mean field theory of the Mott-Anderson transition

We present a theory for disordered interacting electrons that can describe both the Mott and the Anderson transition in the respective limits of zero disorder and zero interaction. We use it to investigate the T=0 Mott-Anderson transition at a fixed electron density, as a the disorder strength is increased. Surprisingly, we find two critical values of disorder W_{nfl} and W_c. For W > W_{nfl}, the system enters a ``Griffiths'' phase, displaying metallic non-Fermi liquid behavior. At even stronger disorder, W=W_c > W_{nfl} the system undergoes a metal insulator transition, characterized by the linear vanishing of both the typical density of states and the typical quasiparticle weight.Comment: 4 pages, 2 figures, REVTEX, eps