Electron-electron and electron-hole pairing in graphene structures

The superconducting pairing of electrons in doped graphene due to in-plane and out-of-plane phonons is considered. It is shown that the structure of the order parameter in the valley space substantially affects conditions of the pairing. Electron-hole pairing in graphene bilayer in the strong coupling regime is also considered. Taking into account retardation of the screened Coulomb pairing potential shows a significant competition between the electron-hole direct attraction and their repulsion due to virtual plasmons and single-particle excitations.Comment: 13 pages with 4 figures; accepted for publication in Phil. Trans. Roy. Soc.

S\mathcal{S}-Matrix of Nonlocal Scalar Quantum Field Theory in the Representation of Basis Functions

Nonlocal quantum theory of one-component scalar field in $D$-dimensional Euclidean spacetime is studied in representations of $\mathcal{S}$-matrix theory for both polynomial and nonpolynomial interaction Lagrangians. The theory is formulated on coupling constant $g$ in the form of an infrared smooth function of argument $x$ for space without boundary. Nonlocality is given by evolution of Gaussian propagator for the local free theory with ultraviolet form factors depending on ultraviolet length parameter $l$. By representation of the $\mathcal{S}$-matrix in terms of abstract functional integral over primary scalar field, the $\mathcal{S}$ form of a grand canonical partition function is found. And, by expression of $\mathcal{S}$-matrix in terms of the partition function, the representation for $\mathcal{S}$ in terms of basis functions is obtained. Derivations are given for discrete case where basis functions are Hermite functions, and for continuous case where basis functions are trigonometric functions. The obtained expressions for the $\mathcal{S}$-matrix are investigated within the framework of variational principle based on Jensen inequality. Equations with separable kernels satisfied by variational function $q$ are found and solved, yielding results for both the polynomial theory $\varphi^{4}$ and the nonpolynomial sine-Gordon theory. A new definition of the $\mathcal{S}$-matrix is proposed to solve additional divergences which arise in application of Jensen inequality for the continuous case. Analytical results are illustrated numerically. For simplicity of numerical calculation: the $D=1$ case is considered, and propagator for the free theory $G$ is in the form of Gaussian function typically in the Virton-Quark model. The formulation for nonlocal QFT in momentum $k$ space of extra dimensions with subsequent compactification into physical spacetime is discussed.Comment: 38 pages, 18 figures; v2: significant text editing; v3: text and plots edited, references and acknowledgments added; prepared for the special issue of the journal Particles in memory of G.V. Efimo

Nonlocal Scalar Quantum Field Theory: Functional Integration, Basis Functions Representation and Strong Coupling Expansion

Nonlocal QFT of one-component scalar field $\varphi$ in $D$-dimensional Euclidean spacetime is considered. The generating functional (GF) of complete Green functions $\mathcal{Z}$ as a functional of external source $j$, coupling constant $g$, and spatial measure $d\mu$ is studied. An expression for GF $\mathcal{Z}$ in terms of the abstract integral over the primary field $\varphi$ is given. An expression for GF $\mathcal{Z}$ in terms of integrals over the primary field and separable Hilbert space (HS) is obtained by means of a separable expansion of the free theory inverse propagator $\hat{L}$ over the separable HS basis. The classification of functional integration measures $\mathcal{D}\left[\varphi\right]$ is formulated, according to which trivial and two nontrivial versions of GF $\mathcal{Z}$ are obtained. Nontrivial versions of GF $\mathcal{Z}$ are expressed in terms of $1$-norm and $0$-norm, respectively. The definition of the $0$-norm generator $\varPsi$ is suggested. Simple cases of sharp and smooth generators are considered. Expressions for GF $\mathcal{Z}$ in terms of integrals over the separable HS with new integrands are obtained. For polynomial theories $\varphi^{2n},\, n=2,3,4,\ldots,$ and for the nonpolynomial theory $\sinh^{4}\varphi$, integrals over the separable HS in terms of a power series over the inverse coupling constant $1/\sqrt{g}$ for both norms ($1$-norm and $0$-norm) are calculated. Critical values of model parameters when a phase transition occurs are found numerically. A generalization of the theory to the case of the uncountable integral over HS is formulated. A comparison of two GFs $\mathcal{Z}$, one in the case of uncountable HS integral and one obtained using the Parseval-Plancherel identity, is given.Comment: 26 pages, 2 figures; v2: significant additions in the text; prepared for the special issue "QCD and Hadron Structure" of the journal Particles; v3: minimal corrections; v4: paragraphs added related to Reviewer comment

Cooper pairing of electrons and holes in graphene bilayer: Correlation effects

Cooper pairing of spatially separated electrons and holes in graphene bilayer is studied beyond the mean-field approximation. Suppression of the screening at large distances, caused by appearance of the gap, is considered self-consistently. A mutual positive feedback between appearance of the gap and enlargement of the interaction leads to a sharp transition to correlated state with greatly increased gap above some critical value of the coupling strength. At coupling strength below the critical, this correlation effect increases the gap approximately by a factor of two. The maximal coupling strength achievable in experiments is close to the critical value. This indicated importance of correlation effects in closely-spaced graphene bilayers at weak substrate dielectric screening. Another effect beyond mean-field approximation considered is an influence of vertex corrections on the pairing, which is shown to be very weak.Comment: 6 pages, 5 figures; some references were adde

GENETIC POLYMORPHISM OF MYCOBACTERIUM TUBERCULOSIS IN PATIENTS WITH TUBERCULOSIS AND HUMAN IMMUNODEFICIENCY VIRUS INFECTION IN EASTEN SIBERIA

A total 61 randomly selected strains of M. tuberculosis were genotyped by the 12 loci of MIRU-VNTR. It was shown the predominance of the Beijing genetic group (78,4 %) in population of mycobacterium from the patients with tuberculosis and. human immunodeficiency virus infection in Irkutsk region and. Buryatia. Multidrug resistance was observed in 34,4 % of the studied strains without significant differences among representatives of Beijing and non-Beijing

COMPREHENSIVE EPIDEMIOLOGICAL ANALYSIS OF THE TUBERCULOSIS SITUATION AMONG THE DIFFERENT ETHNIC GROUPS OF THE BURYATIA

Comprehensive epidemiological analysis of tuberculosis in the Republic of Buryatia (RB), including among different ethnicgroups (Russian, Buryat, Evenk) presents in the article. Assessment of the epidemiological situationfor 1994-2012 was examined on various parameters (incidence, prevalence and mortality). It was found that the epidemiological situation in RB in the last twenty years were characterized by high incidence of tuberculosis when compared with similar data for Russia as a whole (mean annual incidence 148,1 ± 6,90/0000 и 77.6 ± 2,10/0000 respectively). Among the various ethnic groups living in the RB, the most unfavorable epidemiological indicators identified for the Buryat population. "Safely" group of the population was Evenki. For each of the studied ethnic groups have been identified areas of tuberculosis risk, which had its own characteristics

HCV Infection in the Republic of Sakha (Yakutia) and Its Role of Genotypes in Clinical Outcomes of the Disease

Aim of the research. To study the epidemic manifestations of HCV infection in the Republic of Sakha (Yakutia) in order to develop recommendations for improving the effectiveness and quality of treatment and prevention measures. Materials and methods. The paper uses materials from the official statistics of the Territorial Department of Rospotrebnadzor of the Republic of Sakha (Yakutia) for 1994–2018, and data from the electronic register «Chronic viral hepatitis in the RS (Ya)» (2019). Molecular and biological studies of the genotype of the hepatitis C virus were performed jointly on the basis of the Federal state budgetary Institution «Central research Institute of epidemiology» of Rospotrebnadzor (2007–2011, n = 75). To assess the epidemiological situation, the rate of increase in morbidity is calculated on the basis of data equalized by the method of least squares. Statistical processing was performed using the SPSS 17 program. The critical significance level is assumed to be 0.05. Results. Thus, the study of long-term dynamics of the incidence of viral hepatitis shows that in the Republic of Sakha (Yakutia) a consistently high level of incidence of HCV with adverse trends in the development of the epidemic process remains. Analysis of the distribution of different variants of HCV genotypes allowed us to establish the prevalence of genotype 1b, which can determine the high frequency of cirrhosis and primary liver cancer. The current situation in the Republic regarding the incidence of viral hepatitis requires detailed monitoring, improvement of epidemiological surveillance and introduction of modern treatment methods. It is also necessary to improve the quality of health education among the population of the Republic