Antiferromagnetic and superconducting states in the three-band two-dimensional repulsive Hubbard model

The three-band two-dimensional repulsive Hubbard model in the formalism of the temperature Green function is investigated. The applicability of the weak coupling approach at the values of the dimensionless coupling constant U/t≈10–11 is justified. The normal state, the antiferromagnetic state with Neel magnetic ordering on the “copper” sublattice, and the superconducting state with nontrivial Cooper pairing in channels with odd angular momenta are studied. The possibility of other magnetic states in the model is discussed. Bibliography: 20 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 209, 1994, pp. 194–228. Translated by K. Malyshev.     

Relationships between Electrodynamic and Quantum-Mechanical Parameters in the Theory of Quantum Transitions

Relationships between the electrodynamic (wave propagation constants) and quantum-mechanical parameters (probability of induced transitions) of interaction between energy quanta and particles of the medium are derived for dipole and paramagnetic interaction types. It is demonstrated that quantum-mechanical parameters are generally complex.     

Colossal magnetoresistance of the Sm1−x SrxMnO3 system

The results of investigating the temperature dependence of the resistivity, the differential magnetic susceptibility, and the magnetoresistance of a partially substituted perovskite Sm_1−x Sr_xMnO₃ (x=0.16–0.4) are presented. Colossal intrinsic magnetoresistance, reaching 90% in an external magnetic field of 30 kOe, is discovered in the compound with x=0.30 at 77 K. Fiz. Tverd. Tela (St. Petersburg) 39, 1831–1832 (October 1997)     

Spin interaction with an ideal Fermi gas

We consider the equilibrium dynamics of a system consisting of a spin interacting with an ideal Fermi gas on the lattice , 3. We present two examples: when this system is unitarily equivalent to an ideal Fermi gas or to a spin in an ideal Fermi gas without interaction between them.     

Enantioselective reduction of C=O and C=N bonds by TADDOL-containing aluminum hydride reagents based on NaAlH4 and AlH3

Prochiral substrates (alkyl aryl ketones, cyclopropyl methyl ketone, 1-indanone, 1-tetralone, ethyl 2-oxo-4-phenylbutyrate, and N-(diphenylphosphinyl)acetophenoneimine) were subjected to asymmetric reduction with aluminum hydride reagents, which were prepared by modifications of NaAlH₄ or AlH₃ with chiral ,,","-tetraaryl-1,3-dioxolane-4,5-dimethanols (TADDOL). The effects of the nature of the substituents in TADDOL, the structure of the prochiral substrate, and the reaction conditions on the stereochemistry of reduction were investigated. The highest enantioselectivity (70—90% ee) was achieved upon reduction of alkyl aryl ketones and N-(diphenylphosphinyl)acetophenoneimine with NaAl(TADDOLate)H₂ in THF or diglyme at a temperature from –70 to –20 °C. The mechanism of asymmetric induction in the reduction reactions of ketones with aluminum hydride reagents is discussed. The stereochemical results of reduction were explained by comparing three-dimensional models of the most probable transition states.     

Low-temperature dynamics of weakly localized Frenkel excitons in disordered linear chains

We calculate the temperature dependence of the fluorescence Stokes shift and the fluorescence decay time in linear Frenkel exciton systems resulting from the thermal redistribution of exciton population over the band states. The following factors, relevant to common experimental conditions, are accounted for in our kinetic model: (weak) localization of the exciton states by static disorder, coupling of the localized excitons to vibrations in the host medium, a possible nonequilibrium of the subsystem of localized Frenkel excitons on the time scale of the emission process, and different excitation conditions (resonant or nonresonant). A Pauli master equation, with microscopically calculated transition rates, is used to describe the redistribution of the exciton population over the manifold of localized exciton states. We find a counterintuitive nonmonotonic temperature dependence of the Stokes shift. In addition, we show that depending on experimental conditions, the observed fluorescence decay time may be determined by vibration-induced intraband relaxation, rather than radiative relaxation to the ground state. The model considered has relevance to a wide variety of materials, such as linear molecular aggregates, conjugated polymers, and polysilanes.     

A New Proof of a Result Concerning a Complete Description of $$ (n,n + 2) $$ -Graphs with Maximum Value of the Hosoya Index

Mathematical Notes - The Hosoya index is an important topological index of graphs defined as the number of their matchings. At present, for any $$ n $$ and $$ k \in \{- 1,0,1,2 \}$$ , all connected...     

Distribution of integral points on some hyperboloids of one sheet

Results of B. F. Skubenko (Izv. Akad. Nauk SSSR, Ser. Mat.,26, 721–752 (1962)) are generalized to indefinite ternary quadratic formsf(x)=f ₀(Cx), which are contained in the simplest formf ₀(x)=x ₁ x ₃–x _r ^e We prove that the integral points on the hyperboloid of one sheetf(x)=m,m<0, are uniformly distributed over area (in the sense of hyperbolic metric) and over residue classes for given modulus.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 121, pp. 83–93, 1983.