Thermoelectric effect in superconducting alloys

Zubarev's nonequilibrium statistical operator method is used to construct a theory of the thermoelectric effect in superconductors in a form independent of the ratio of the electron mean free path to the correlation length of the superconductor. The thermoelectric effect is studied for some models of superconducting alloys.In memory of D. N. ZubarevInstitute of Applied Physics, Moldovan Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 97, No. 1, pp. 44–52, October, 1993.     

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.     

Calculation of Berry's phase in squeezed states

A simple method based on generalized coherent states is proposed for calculation of Berry's phase. In this paper we calculate Berry's phase for a translated oscillator in standard coherent states as well as Berry's phase in squeezed states and spin coherent states, i.e., coherent states for the SU(1, 1) and SU(2) groups, respectively.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 169, pp. 51–59, 1988.     

Feromagnetism in the single-band Hubbard model in the limit of strong correlations

Institute of Metal Physics, Urals Branch, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 81, No. 3, pp. 434–440, December, 1989.     

Self-consistent cluster theory of the electron spectra of alloys

A method of self-consistent cluster expansion for the mass operator of the Green's function with allowance for short-and longrange order in alloys is proposed. A self-consistent system of equations for the coherent potential and the mass operator is obtained in the approximation in which the contributions of processes involving electron scattering by clusters of three or more atoms are ignored. The contributions of the scattering processes to the Green's function of the alloy decrease with increasing number of particles in a cluster and can be estimated by means of a certain small parameter. Analytic and numerical investigations of the energy dependence of the density of single-electron states of a binary alloy are made for different values of the parameter of the short-range order.Institute of Metal Physics, Ukrainian Academy of Sciences; Kiev University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 97, No. 2, pp. 304–319, November, 1993.     

Mutual transition of Andreev and Majorana bound states in a superconducting gap

Theoretical and Mathematical Physics - Using the Bogoliubov–de Gennes Hamiltonian, we analytically study two models with superconducting order, the p-wave model with an impurity potential and...     

The integrated density of states in strong magnetic fields

We consider three-dimensional Schrödinger operators with constant magnetic fields and ergodic electric potentials. We study the strong magnetic field asymptotic behaviour of the integrated density of states, distinguishing between the asymptotics far from the Landau levels, and the asymptotics near a given Landau level.     

Cross approximation in tensor electron density computations

We propose new tensor approximation algorithms for certain discrete functions related with Hartree–Fock/Kohn–Sham equations. Given a canonical tensor representation for the electron density function (for example, produced by quantum chemistry packages such as MOLPRO), we obtain its Tucker approximation with much fewer parameters than the input data and the Tucker approximation for the cubic root of this function, which is part of the Kohn–Sham exchange operator. The key idea is in the fast and accurate prefiltering of possibly large‐scale factors of the canonical tensor input. The new algorithms are based on the incomplete cross approximation method applied to matrices and tensors of order 3 and outperform other tools for the same purpose. First, we show that the cross approximation method is robust and much faster than the singular value decomposition‐based approach. As a consequence, it becomes possible to increase the resolution of grid and the complexity of molecules that can be handled by the Hartree–Fock chemical models. Second, we propose a new fast approximation method for f^1/3(x, y, z), based on the factor prefiltering method for f(x, y, z) and certain mimic approximation hypothesis. Third, we conclude that the Tucker format has advantages in the storage and computation time compared with the ubiquitous canonical format. Copyright © 2009 John Wiley & Sons, Ltd.     

Continuity properties of the integrated density of states on manifolds

We first analyze the integrated density of states (IDS) of periodic Schrödinger operators on an amenable covering manifold. A criterion for the continuity of the IDS at a prescribed energy is given along with examples of operators with both continuous and discontinuous IDS. Subsequently, alloy-type perturbations of the periodic operator are considered. The randomness may enter both via the potential and the metric. A Wegner estimate is proven which implies the continuity of the corresponding IDS. This gives an example of a discontinuous “periodic” IDS which is regularized by a random perturbation.     

Average density of states for Hermitian Wigner matrices

We consider ensembles of N×N Hermitian Wigner matrices, whose entries are (up to the symmetry constraints) independent and identically distributed random variables. Assuming sufficient regularity for the probability density function of the entries, we show that the expectation of the density of states on arbitrarily small intervals converges to the semicircle law, as N tends to infinity.