Boundary-value problem for nonlinear Schrödinger equation

Leningrad State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 79, No. 3, pp. 334–346, June, 1989.     

Interaction of 2-chloroquinoline- 3-carbaldehydes with 2-hetaryl- acetonitriles

The interaction of 2-chloroquinoline-3-carbaldehydes with 1H-benzimidazol-2-ylacetonitriles and 1-benzyl-1H-imidazol-2-ylacetonitrile has been studied. It was shown that products of condensation at the methylene group are formed under mild conditions. Carrying out the reaction under more forcing conditions leads to an intramolecular nucleophilic substitution of the chlorine atom and the formation of cyclic ionic compounds (in the case of N-substituted hetarylacetonitriles), which are subsequently dealkylated.     

On Bethe Vectors for the XXZ Model at Roots of Unity

We give a construction of creation operators responsible for appearance of Bethe vectors with the same eigenvalues of the transfer-matrix for the inhomogeneous arbitrary spin XXZ model at roots of unity with particular quasiperiodic boundary conditions. This construction generalizes a similar one, recently obtained by K. Fabricius and B. M. McCoy, for the homogeneous six-vertex model with periodic boundary conditions. Even in the latter case, the given proofs for the main formulas are simpler than the original one. Bibliography: 6 titles.     

Trace determination of β-Chlorovinyldichloroarsine (Lewisite) in water, soil, and construction materials by gas chromatography

A method is proposed for the trace determination of β-chlorovinyldichloroarsine (lewisite) in water, soil, and construction materials by gas chromatography with the conversion of the test compound to acetylene     

Quantum Maps with Memory from Generalized Lindblad Equation

In this paper, we proposed the exactly solvable model of non-Markovian dynamics of open quantum systems. This model describes open quantum systems with memory and periodic sequence of kicks by environment. To describe these systems, the Lindblad equation for quantum observable is generalized by taking into account power-law fading memory. Dynamics of open quantum systems with power-law memory are considered. The proposed generalized Lindblad equations describe non-Markovian quantum dynamics. The quantum dynamics with power-law memory are described by using integrations and differentiation of non-integer orders, as well as fractional calculus. An example of a quantum oscillator with linear friction and power-law memory is considered. In this paper, discrete-time quantum maps with memory, which are derived from generalized Lindblad equations without any approximations, are suggested. These maps exactly correspond to the generalized Lindblad equations, which are fractional differential equations with the Caputo derivatives of non-integer orders and periodic sequence of kicks that are represented by the Dirac delta-functions. The solution of these equations for coordinates and momenta are derived. The solutions of the generalized Lindblad equations for coordinate and momentum operators are obtained for open quantum systems with memory and kicks. Using these solutions, linear and nonlinear quantum discrete-time maps are derived.