Quantum holography upon resonant adiabatic interaction of fields with an atomic medium in a Λ-configuration

We study the quantum memory protocol for spatially multimode light based on an atomic ensemble in the Λ-configuration. We analytically solve a system of partial differential equations that describe the evolution of the medium and field for the case where the interaction time considerably exceeds the lifetime of the excited state. This time ratio makes it possible to apply the adiabatic approximation. Unlike problems aimed at storage the time profile of the signal field, we propose optimizing the relation between the writing and reading times and the optical density of the medium, which ensures a high retrieval efficiency of the quantum image.     

Cu(II)-alkyl chlorocomplexes: stable compounds or transients? DFT prediction of their structure and EPR parameters

DFT calculations were used for studying the structure and reactivity of organocuprates(II) usually considered as intermediates with very weak Cu-C bond. It was found that calculated principal g-tensor values of model compounds RCu(II)Cl(2(-)) are similar to the experimentally found values for organocopper product of photolysis of quaternary ammonium tetrachlorocuprates. The calculations confirm that the most of organocuprates(II) could be stable at ambient conditions, and short lifetimes of organocuprates(II) in solutions or soft matrices are caused by their high reactivity in various bimolecular processes; the rate of those may be close to the rate of diffusion controlled reactions. The charges, spin densities, and d-orbital populations of the Cu atom in them are typical for bivalent copper complexes. Natural bond orbital analysis of organochlorocuprates(II) confirms the formation of polar σ-bond between copper and carbon atoms.     

Series ∑F(m)qm,where F(m) is the number of odd classes of binary quadratic forms of determinant −m

Consideration of the analytic continuation of the Eisenstein series of weight 3/2 for the group ₀(4) leads to a new proof of Mordell's formula connecting the values X()= _m=1 F(m)e^im, Im > 0, and (–1/). The behavior of the function () for ₀(4) is examined by the same method.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 64, pp. 69–79, 1976.     

Exceptional Integers for Binary Quadratic Forms

An integer m is said to be exceptional for a binary quadratic form if m is representable by a form from the genus of but not by the form itself. An asymptotic distribution law for exceptional integers is proved. Bibliography: 3 titles.     

Application of spherical functions to a certain problem in the theory of quadratic forms

The problem regarding the number of integral points on multidimensional ellipsoids is investigated with the aid of modular forms. In the paper we consider the simplest special case of the following problem: one considers a multidimensional sphere and as a domain on it one selects a cap. The precise result is formulated in the following manner: let r(n) be the number of the representations of n by a sum of squares, 0n₁, 2 n; the expression for K(A), 4, is given in the paper. It is also shown that one can refine somewhat the results on the distribution of integral points on multidimensional ellipsoids, obtained by A. V. Malyshev by the circular method, remaining within the framework of the same methods.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 144, pp. 38–45, 1985.We express our gratitude to M. A. skopina for a consultatin regarding the theory of multiple fourier series     

The Distribution of Values of the Hecke L-Functions at 1

Let S₂(q) be the set of primitive forms in the space S₂(Γ₀(q)) of holomorpic Γ₀(q)-cusp forms of weight 2. Let f ∈ S₂(q) and let L_f(S) be the L-function of f(z). It is proved that the set {log L_f(1), f ∈ S₂(q)} has a limit distribution function. The rate of convergence to this limit function is estimated. Bibliography: 10 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 314, 2004, pp. 15–32.