Related papers: The Falicov-Kimball model
The review is based on the author's papers since 1985 in which a new approach to the separation of variables (\SoV) has being developed. It is argued that \SoV, understood generally enough, could be the most universal tool to solve…
The survey of the current state of the theory of Krichever-Novikov algebras including new results on local central extensions, invariants, representations and casimir operators.
An introductory review of Classical Statistical Mechanics
In the present paper Q-ball solutions in the Wick--Cutkosky model are examined in detail. A remarkable feature of the Wick--Cutkosky model is that it admits analytical treatment for the most part of the analysis of Q-balls, which allows one…
In this article, the weakest possible theorem providing a foundation for the Hilbert space formalism of quantum theory is stated. The necessary postulates are formulated, and the mathematics is spelt out in detail. It is argued that, from…
This paper is a very brief introduction to idempotent mathematics and related topics.
A dynamical model is proposed for isotropic turbulence driven by steady forcing that yields a viscosity independent dynamics for the small-scale (inertial) regime. This reproduces the Kolmogorov spectrum for the two-point velocity…
It is shown that the recent criticism of Brevik et al. (hep-th/0004041) is in error.
It is long known that the best single-site coherent potential approximation (CPA) falls short of describing Anderson localization (AL). Here, we study a binary alloy disorder (or equivalently, a spinless Falicov-Kimball (FK)) model and…
Some aspects and applications of $ \sigma$-models in particle and condensed matter physics are briefly reviewed.
A semiclassical model, based on a solution of the Vlasov equation for finite systems with moving-surface, is employed to study the isoscalar dipole modes in nuclei. It is shown that, by taking into account the surface degree of freedom, it…
Contribution to the Encyclopedia of Mathematical Physics (Elsevier, 2006): a brief and (hopefully) pedagogical introduction to quantum field theory models describing particles in external fields is presented. Following the instructions, the…
A complete classification of space-time models is presented, which admit the privileged coordinate systems, where the Hamilton-Jacobi equation for a test particle is integrated by the method of complete separation of variables with…
An expository article on Turaev surfaces written for "A Concise Encyclopedia of Knot Theory," to appear.
To appear to MCMC handbook, S. P. Brooks, A. Gelman, G. Jones and X.-L. Meng (eds), Chapman & Hall.
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.
This survey paper is an expanded version of lectures given at the Clay Mathematics Academy ; see http://www.claymath.org/programs/outreach/academy/colloquium2005.php These lectures were intended to very young (and motivated) college…
The maximum principle for holomirphic functions in the quantum ball is formulated. A proof can be found in [8] (see the bibliography).
An informal guide to the history of Heisenberg's matrix mechanics. It is designed for mathematicians with only a minimal background in either physics or geometry, and it is based upon Heisenberg's original arguments.
Three approaches to the derivation of the classical electromagnetic modes of a rectangular cavity are described. In so doing, some apparent errors in a widely-used physics text are pointed out.