Self-consistent theory of electron correlation in the Hubbard model

Theoretical and Mathematical Physics -     

On superconductivity in the three-band two-dimensional repulsive hubbard model

The three-band Hubbard model, known also as the Emery model, is investigated in the framework of thermal Green functions. It is shown that antiferromagnetic and superconductive states can exist in this model at appropriate doping and sufficiently low temperatures. In the two-dimensional repulsive case under consideration, superconductivity turns out to be possible due to the closeness of the Fermi level to one of the energy function saddle points and the pairing occurs in channels with odd angular momenta.Deceased.Published in Teoreticheskaya i Matematicheskaya Fizika, Vol. 105, No. 1, pp. 149–162, October, 1995.     

Integration over a superalgebra in the hubbard model with a strong correlation

We represent the partition function of the Hubbard model with a strong Coulomb repulsion as a path integral over auxiliary Grassman variables. An approximate analysis of the phase transitions demonstrates that (1) the system is an antiferromagnetic insulator when the doping constant is small, (2) when t/U, the system is a ferromagnetic metal if U/t > 10, and a superconducting metal if U/t 10.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 107, No. 2, pp. 269–287, May, 1996.Translated by A. M. Semikhatov.     

Solutions of two-dimensional Schrödinger-type equations in a magnetic field

We use the method of dressing by a linear operator of general form to construct new solutions of Schrödinger-type two-dimensional equations in a magnetic field. In the case of a nonunit metric, we integrate the class of solutions that admit a variable separation before dressing. In particular, we show that the ratio of the coefficients of the differential operators in the unit metric case satisfies the Hopf equation. We establish a relation between the solutions of the two-dimensional eikonal equation with the unit right-hand side and solutions of the Hopf equation.     

Quantum corrections to the conductivity of a two-dimensional disordered system in a strong magnetic field

A system of noninteracting electrons moving in a magnetic field and a field of randomly distributed impurities is considered. An exact expression is obtained for the sum of the series of maximally crossed diagrams; it is valid in an arbitrary magnetic field. It is shown that in the two-dimensional case the relative magnitude of the corrections to the conductivity due to this series reaches 60% in the center of the lower Landau sub-band.Physicotechnical Institute of the Urals Branch of the Russian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 94, No. 3, pp. 486–495, March, 1993.     

Self-consistent approximation in the Ising model of pure and dilute magnets using a pair correlation

Theoretical and Mathematical Physics - We construct a self-consistent approximation for calculating the magnetization and Curie temperature in the Ising model on an arbitrary lattice based on using...     

Superconductivity in the Fröhlich two-dimensional model with an arbitrary carrier concentration

Using the Fröhlich Hamiltonian, we obtain self-consistent equations for the energy gap and the chemical potential. Using these equations, we can analyze the superconductivity properties of the system for an arbitrary carrier concentration. We consider weak, intermediate, and strong intermediate, and strong interactions between fermions and observe the transition from the Cooper coupling to the local-pair regime in the indirect-interaction model.     

Global existence of weak solutions for two-dimensional semilinear wave equations with strong damping in an exterior domain

We consider two-dimensional mixed problems in an exterior domain for a semilinear strongly damped wave equation with a power-type nonlinearity |u|^p${\left|u\right|}^p$. If the initial data have a small weighted energy, we shall derive a global existence and energy decay results in the case when the power p$p$ of the nonlinear term satisfies p>6$p>6$.     

System of differential equations with a strong turning point

The uniform asymptotics of a solution of a system of singularly perturbed differential equations with strong turning point is constructed. We study the case where the boundary operator is analytic with respect to a small parameter.     

Resonance in equations with a diagonal field

Let A be a real square matrix, and let J?$\text{R}$ be an interval not containing an eigenvalue of A. Is A–D nonsingular for all diagonal matrices D with entries d_i ∈J? This holds if A is symmetric, but is not true in general. We prove a necessary condition and indicate implications for an equation with a diagonal field.     

Integrable model of a two-dimensional singular spherical oscillator in a constant magnetic field

We propose an analogue of a two-dimensional singular oscillator (Smorodinsky-Winternitz oscillator) on a sphere, which is exactly solvable in the classical sense both without and with a constant magnetic field. We find the explicit classical solutions. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 1, pp. 131–137, July, 2008.     

Derivation of lower critical magnetic field for anisotropic Ginzburg-Landau model in superconductivity

In this paper, the authors discuss the vortex structure of an anisotropic Ginzburg-Landau model for superconducting thin film proposed by Du. We obtain the estimate for the lower critical magnetic field $ H_{C_1 } $ H_{C_1 } which is the first critical value of h _ex corresponding to the first phase transition in which vortices appear in the superconductor. We also find local minimizers of the anisotropic superconducting thin film with a large parameter κ, and for the applied magnetic field near the critical field we discuss the asymptotic behavior of the local minimizers.     

Finite element analysis of a current density-electric field formulation of Bean's model for superconductivity

We study a current density–electric field formulationof Bean's model for the experimental set-up of an infinitelylong cylindrical superconductor subject to a transverse magneticfield. We introduce a fully practical finite-element approximationof the model and prove an error between the exact solution andthe approximate solution for the current density of order (h+ t)^1/2. Numerical simulations for a variety of given sourcecurrents are presented.     

Integral equations of a two-dimensional lightguide

An integral equation describing oscillations of a two-dimensional periodic lightguide is studied. The integral operator is an analytic function of a spectral parameter. The homogenous integral equation has only the zero solution for all values of the spectral parameter expect for some isolated values. Bibliography: 9 titles. Translated fromProblemy Matematicheskogo Analiza, No. 18, 1998, pp. 78–84.