Quantization of the Riemann Zeta-Function and Cosmology

Quantization of the Riemann zeta-function is proposed. We treat the Riemann zeta-function as a symbol of a pseudodifferential operator and study the corresponding classical and quantum field theories. This approach is motivated by the theory of p-adic strings and by recent works on stringy cosmological models. We show that the Lagrangian for the zeta-function field is equivalent to the sum of the Klein-Gordon Lagrangians with masses defined by the zeros of the Riemann zeta-function. Quantization of the mathematics of Fermat-Wiles and the Langlands program is indicated. The Beilinson conjectures on the values of L-functions of motives are interpreted as dealing with the cosmological constant problem. Possible cosmological applications of the zeta-function field theory are discussed.Comment: 14 pages, corrected typos, references and comments adde

Semiclassical measures and the Schroedinger flow on Riemannian manifolds

In this article we study limits of Wigner distributions (the so-called semiclassical measures) corresponding to sequences of solutions to the semiclassical Schroedinger equation at times scales $\alpha_{h}$ tending to infinity as the semiclassical parameter $h$ tends to zero (when $\alpha _{h}=1/h$ this is equivalent to consider solutions to the non-semiclassical Schreodinger equation). Some general results are presented, among which a weak version of Egorov's theorem that holds in this setting. A complete characterization is given for the Euclidean space and Zoll manifolds (that is, manifolds with periodic geodesic flow) via averaging formulae relating the semiclassical measures corresponding to the evolution to those of the initial states. The case of the flat torus is also addressed; it is shown that non-classical behavior may occur when energy concentrates on resonant frequencies. Moreover, we present an example showing that the semiclassical measures associated to a sequence of states no longer determines those of their evolutions. Finally, some results concerning the equation with a potential are presented.Comment: 18 pages; Theorems 1,2 extendend to deal with arbitrary time-scales; references adde

Next stage of search for 2K(2ν\nu)-capture of 78^{78}Kr

A technique to search for 2K-capture of $^{78}$Kr with large low-background proportional counter filled with an enriched in $^{78}$Kr up to 99.8% sample of Krypton at a pressure of 4.51 is described in this paper. The results of first measurements are presented. Analysis of data collected during 159 hours yielded new limit to the half-life of $^{78}$Kr with regard to 2K-capture (T$_{1/2}\geq6\cdot10^{21}$ yr (90% C.L.)). Sensitivity of the facility to the process for one year of measurement was evaluated to be $\texttt{S}=1.0\cdot10^{22}$ yr (90% C.L.).Comment: 4 pages, 5 figures; talk at the NANP'05 Conference; submitted to Phys. At. Nuc

Essential self-adjointness of magnetic Schr\"odinger operators on locally finite graphs

We give sufficient conditions for essential self-adjointness of magnetic Schr\"odinger operators on locally finite graphs. Two of the main theorems of the present paper generalize recent results of Torki-Hamza.Comment: 14 pages; The present version differs from the original version as follows: the ordering of presentation has been modified in several places, more details have been provided in several places, some notations have been changed, two examples have been added, and several new references have been inserted. The final version of this preprint will appear in Integral Equations and Operator Theor

Construction of Polymeric Antigenic Diagnosticum Based on <i>Vibrio cholera</i> О1 Lipopolysaccharide

Representatives of the genus Vibrio cholerae differ in the structure of lipopolysaccharide, in particular, its O-polysaccharide chains (O-antigen), which determines the serological specificity of vibrios. Currently, the water-phenolic method is used to obtain the lipopolysaccharide preparation. However, this technique relates to harsh chemical methods, leads to a change in original molecular organization of biopolymer, violating its structure and biological properties. Modern technologies in the development of diagnostic kits for the immunosuspension reaction of volume agglomeration allow for obtaining synthetic carriers with different reaction groups on the particle surface capable to bind antigens/antibodies. The aim of this study was to construct cholera antigenic polymeric diagnostic kit based on the lipopolysaccharide of Vibrio cholerae O1 serogroup. Materials and methods. The lipopolysaccharide was used as a sensitizer obtained through the author's modification of enzymatic purification from the cell membranes of Vibrio cholerae using ultrasonic disintegration. Results and discussion. The resulting sensitin contains small impurities of protein (1.5 %) and nucleic acids (0.1 %). Diagnosticum is characterized by high analytical sensitivity in agglomeration reaction with commercial and experimental rabbit serum to Vibrio cholerae O1 serogroup (1:640 - 1:5120) and analytical specificity (the diagnosticum does not interact with heterologous sera, with serums to pathogens of acute intestinal infections, as well as with sera from healthy donors). A polymeric antigenic cholera diagnosticum designed to detect antibodies to lipopolysaccharide of Vibrio cholerae in the blood serum of patients who were ill, suspected of the disease or vaccinated people has been constructed

Oxygen transport in Pr nickelates: Elucidation of atomic-scale features

Pr2NiO4+δ oxide with a layered Ruddlesden–Popper structure is a promising material for SOFC cathodes and oxygen separation membranes due to a high oxygen mobility provided by the cooperative mechanism of oxygen migration involving both interstitial oxygen species and apical oxygen of the NiO6 octahedra. Doping by Ca improves thermodynamic stability and increases electronic conductivity of Pr2 − xCaxNiO4+δ, but decreases oxygen mobility due to decreasing the oxygen excess and appearing of 1–2 additional slow diffusion channels at x ≥ 0.4, probably, due to hampering of cooperative mechanism of migration. However, atomic-scale features of these materials determining oxygen migration require further studies. In this work characteristics of oxygen diffusion in Pr2 − xCaxNiO4+δ (x = 0–0.6) are compared with results of the surface analysis by X-ray photoelectron spectroscopy and modeling of the interstitial oxygen migration by the plane-wave density functional theory calculations. According to the X-ray photoelectron spectroscopy data, the surface is enriched by Pr for undoped sample and by Ca for doped ones. The O1s peak at ~531 eV corresponding to a weakly bound form of surface oxygen located at Pr cations disappears at ~500 °C. Migration of interstitial oxygen was modeled for a I4/mmm phase of Pr2NiO4+δ. The interstitial oxygen anion repulses the apical one in the NiO6 octahedra pushing it into the tetrahedral site between Pr cations. The calculated activation barrier of this migration is equal to 0.585 eV, which reasonably agrees with the experimental value of 0.83 eV obtained by the oxygen isotope exchange method. At the same time, for the model compound Ca2NiO4+δ, obtained by isomorphic substitution of Pr by Ca in Pr2NiO4+δ, calculations implied formation of the peroxide ion comprised of interstitial and lattice oxygen species not revealed in the case of incomplete substitution (up to PrCaNiO4+δ composition). Hence, calculations in the framework of the plane-wave density functional theory provide a realistic estimation of specificity of oxygen migration features in Pr2NiO4+δ doped by alkaline-earth metals. © 2019 Elsevier B.V.Russian Science Foundation, RSF: 16-13-00112Support by Russian Science Foundation (Project 16-13-00112 ) is gratefully acknowledged

On the derivation of the t-J model: electron spectrum and exchange interactions in narrow energy bands

A derivation of the t-J model of a highly-correlated solid is given starting from the general many-electron Hamiltonian with account of the non-orthogonality of atomic wave functions. Asymmetry of the Hubbard subbands (i.e. of ``electron'' and ``hole''cases) for a nearly half-filled bare band is demonstrated. The non-orthogonality corrections are shown to lead to occurrence of indirect antiferromagnetic exchange interaction even in the limit of the infinite on-site Coulomb repulsion. Consequences of this treatment for the magnetism formation in narrow energy bands are discussed. Peculiarities of the case of ``frustrated'' lattices, which contain triangles of nearest neighbors, are considered.Comment: 4 pages, RevTe

Quantum Graphs II: Some spectral properties of quantum and combinatorial graphs

The paper deals with some spectral properties of (mostly infinite) quantum and combinatorial graphs. Quantum graphs have been intensively studied lately due to their numerous applications to mesoscopic physics, nanotechnology, optics, and other areas. A Schnol type theorem is proven that allows one to detect that a point belongs to the spectrum when a generalized eigenfunction with an subexponential growth integral estimate is available. A theorem on spectral gap opening for ``decorated'' quantum graphs is established (its analog is known for the combinatorial case). It is also shown that if a periodic combinatorial or quantum graph has a point spectrum, it is generated by compactly supported eigenfunctions (``scars'').Comment: 4 eps figures, LATEX file, 21 pages Revised form: a cut-and-paste blooper fixe

Band spectra of rectangular graph superlattices

We consider rectangular graph superlattices of sides l1, l2 with the wavefunction coupling at the junctions either of the delta type, when they are continuous and the sum of their derivatives is proportional to the common value at the junction with a coupling constant alpha, or the "delta-prime-S" type with the roles of functions and derivatives reversed; the latter corresponds to the situations where the junctions are realized by complicated geometric scatterers. We show that the band spectra have a hidden fractal structure with respect to the ratio theta := l1/l2. If the latter is an irrational badly approximable by rationals, delta lattices have no gaps in the weak-coupling case. We show that there is a quantization for the asymptotic critical values of alpha at which new gap series open, and explain it in terms of number-theoretic properties of theta. We also show how the irregularity is manifested in terms of Fermi-surface dependence on energy, and possible localization properties under influence of an external electric field. KEYWORDS: Schroedinger operators, graphs, band spectra, fractals, quasiperiodic systems, number-theoretic properties, contact interactions, delta coupling, delta-prime coupling.Comment: 16 pages, LaTe