Related papers: The Falicov-Kimball model
Comments on the article "Pulsar dynamics: magnetic dipole model revisited".
We present an exact, unconstrained representation of the electron operators in terms of operators of opposite statistics. We propose a path--integral representation for the $t$-$J$ model and introduce a parameter controlling the…
Metal-insulator transitions are studied within a three-component Falicov-Kimball model which mimics a mixture of one-component and two-component fermionic particles with local repulsive interactions in optical lattices. Within the model the…
This version has been withdrawn. The new and final version is on ArXiv 1103.4878
The more recent paper "Generic strange duality for K3 surfaces" by the authors contains stronger results.
In this paper, Langevin model equation is proposed for Fourier modes of velocity field of isotropic turbulence whose statistical properties are identical to those governed by equations of Self-Consistent-Field (SCF) theory of turbulence [J.…
We argue that our analysis of the J-Q model, presented in Phys. Rev. B 80, 174403 (2009), and based on a field-theory description of coupled dimers, captures properly the strong quantum fluctuations tendencies, and the objections outlined…
In this article we give evaluations of certain series of hyperbolic functions, using Jacobi elliptic functions theory. We also define some new functions that enable us to give characterization of not solvable class of series.
The main result of the paper is a global asymptotic stability result for solutions to the Lifschitz-Slyozov-Wagner (LSW) system of equations. This extends some local asymptotic stability results of Niethammer-Vel\'{a}zquez (2006). The…
This is a survey article concerning applications of Hilbert's metric in the analysis and dynamics of linear and nonlinear mappings on cones. It will appear as a chapter in the "Handbook of Hilbert geometry", ed. G. Besson, A. Papadopoulos…
Correction to Annals of Applied Probability 17 (2007) 781--808 [doi:10.1214/105051607000000032].
This book is a manual for the course of electrodynamics and theory of relativity. It is recommended primarily for students of mathematical departments. This defines its style: I use elements of vectorial and tensorial analysis, differential…
In this short paper, the results of the paper by Drab et al. (Eur. Phys. J. E (2022) 45:79) are described in the framework of wave mechanics and mathematical physics based on common understandings. The attention is focused on properties of…
The three-band Emery model is reduced to a single-particle quantum model of Falicov-Kimball type, by allowing only up-spins to hop, and forbidding double occupation by projection. It is used to study the effects of geometric obstruction on…
The paper is written for Kluwer's Encyclopaedia of Mathematics.
Theory of the Casimir effect is presented in several examples. Casimir - Polder type formulas, Lifshitz theory and theory of the Casimir effect for two gratings separated by a vacuum slit are derived. Equations for the electromagnetic field…
In this article, we give a rough, and so not complete yet, proof of Kashaev's conjecture, that is, the volume conjecture for hyperbolic knots, where the hyperbolicity equations associated to knot diagrams appear as the stationary phase…
The role of mathematical models in physics has for longer been well established. The issue of their proper building and use appears to be less clear. Examples in this regard from relativity and quantum mechanics are mentioned. Comments…
A concise introduction to the Standard Model of fundamental particle interactions is presented.
The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein--Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important…