Correlators of densities in the one-dimensional hubbard model

The one-dimensional Hubbard model with infinitely strong repulsion between electrons is considered. Explicit expressions for the two-point correlators of local densities (dependent on time, temperature, the chemical potential, and the external field) are obtained. Bibliography: 12 titles. Dedicated to O. A. Ladyzhenskaya on the occasion of her jubilee Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 249, 1997, pp. 7–19. Translated by A. G. Izergin and A. G. Pronko.     

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.     

Superconductivity in the hubbard model with deviation from half filling

An equation that determines the critical temperature of the superconducting transition is obtained on the basis of allowance for strong electron correlations. A deviation from half filling of the band is assumed. The equation is manifestly symmetric with respect to replacement of particles by holes.deceasedInstitute of Applied Physics, Moldavian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 92, No. 2, pp. 182–190, August, 1992.     

New diagram technique for the Anderson model

A generalized Wick theorem for the Anderson model is formulated. On this basis, the diagram technique for the temperature Green's function and the thermodynamic potential is developed. Particular attention is paid to the region of strong coupling of an impurity atom with a metal. The Dyson equations are solved and the impurity Green's function is expressed in terms of the mass operator. The contribution to the mass operator and corrections to the energies of localized states are obtained in the second order of perturbation theory.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 109, No. 2, pp. 279–294, November, 1996.     

On the theory of degenerate elliptic equations

Siberian Mathematical Journal -     

A diagram method for the two-band Hubbard model

The two-band Hubbard model is considered within the framework of a diagram technique designed to take strong electronic correlations into account.In memory of Professor D.N. ZubarevInstitute of Applied Physics, Academy of Sciences of Moldova. Published in Teoreticheskaya i Matematicheskaya Fizika, Vol. 97, No. 2, pp. 270–282, November, 1993.     

On the theory of degenerate alternating beltrami equations

The article focuses on the equation A(z)f _z (z) + B(z)f _z?(z) = 0. We aim at the study of the interrelation between the solutions to this equation and the solutions to the appropriate classical Beltrami equation.     

Finite volume methods for degenerate chemotaxis model

A finite volume method for solving the degenerate chemotaxis model is presented, along with numerical examples. This model consists of a degenerate parabolic convection-diffusion PDE for the density of the cell-population coupled to a parabolic PDE for the chemoattractant concentration. It is shown that discrete solutions exist, and the scheme converges.     

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.     

Limit theory for random walks in degenerate time-dependent random environments

We study continuous-time (variable speed) random walks in random environments on ${\mathbb{Z}}^d$, $d\ge 2$, where, at time t, the walk at x jumps across edge $(x,y)$ at time-dependent rate $a_t(x,y)$. The rates, which we assume stationary and ergodic with respect to space–time shifts, are symmetric and bounded but possibly degenerate in the sense that the total jump rate from a vertex may vanish over finite intervals of time. We formulate conditions on the environment under which the law of diffusively-scaled random walk path tends to Brownian motion for almost every sample of the rates. The proofs invoke Moser iteration to prove sublinearity of the corrector in pointwise sense; a key additional input is a conversion of certain weighted energy norms to ordinary ones. Our conclusions apply to random walks on dynamical bond percolation and interacting particle systems as well as to random walks arising from the Helffer–Sjöstrand representation of gradient models with certain non-strictly convex potentials.     

The effective action and the spectrum of collective modes in the antiferromagnetic phase of the three-band repulsive hubbard model

The paper is concerned with the application of path integration (successive integration over “fast” and “slow” variables and the Hubbard-Stratonovich transformation) to the antiferromagnetic state in the three-band, two-dimensional repulsive Hubbard model. It is shown that, in the lowest approximation, the model under consideration is equivalent to the half-filled single-band Hubbard model. The effective action for the collective Bose-fields, the critical temperature of the phase transition, and the spectra of excitations are obtained. Bibliography: 24 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 245, 1997, pp. 216–230. Translated by C. L. Malyshev.