Remarks on the life and research of Roland L. Dobrushin

The life and research work of Professor R.L. Dobrushin (1929-1995) had a profound influence on several areas of probability theory, information theory, and mathematical physics. The paper contains a biographical note, a review of Dobrushin's results, and a list of his publications.Peer Reviewe

Stability of closed gaps for the alternating Kronig-Penney Hamiltonian

We consider the Kronig-Penney model for a quantum crystal with equispaced periodic delta-interactions of alternating strength. For this model all spectral gaps at the centre of the Brillouin zone are known to vanish, although so far this noticeable property has only been proved through a very delicate analysis of the discriminant of the corresponding ODE and the associated monodromy matrix. We provide a new, alternative proof by showing that this model can be approximated, in the norm resolvent sense, by a model of regular periodic interactions with finite range for which all gaps at the centre of the Brillouin zone are still vanishing. In particular this shows that the vanishing gap property is stable in the sense that it is present also for the "physical" approximants and is not only a feature of the idealised model of zero-range interactions. \ua9 2015, Springer Basel

Felix Alexandrovich Berezin and his work

This is a survey of Berezin's work focused on three topics: representation theory, general concept of quantization, and supermathematics.Comment: LaTeX, 27 page

Ground state Euclidean measures for quantum lattice systems on compact manifolds

Albeverio S, Kondratiev Y, Minlos RA, Shchepan'uk GV. Ground state Euclidean measures for quantum lattice systems on compact manifolds. REPORTS ON MATHEMATICAL PHYSICS. 2000;45(3):419-429.Quantum lattice systems with compact spins and nearest-neighbour interactions are considered. The existence and uniqueness of the corresponding ground state Euclidean measures are proved for sufficiently small mass of the particles

Uniqueness problem for quantum lattice systems with compact spins

Albeverio S, Kondratiev Y, Minlos RA, Shchepan'uk GV. Uniqueness problem for quantum lattice systems with compact spins. LETTERS IN MATHEMATICAL PHYSICS. 2000;52(3):185-195.Quantum lattice systems with compact spins and nearest-neighbour interactions are considered. Uniqueness of the corresponding Euclidean Gibbs states is proved uniformly with respect to the temperature, in the case where the particles have a sufficiently small mass

A Class of Hamiltonians for a Three-Particle Fermionic System at Unitarity,

We consider a quantum mechanical three-particle system made of two identical fermions of mass one and a different particle of mass m, where each fermion interacts via a zero-range force with the different particle. In particular we study the unitary regime, i.e., the case of infinite two-body scattering length. The Hamiltonians describing the system are, by definition, self-adjoint extensions of the free Hamiltonian restricted on smooth functions vanishing at the two-body coincidence planes, i.e., where the positions of two interacting particles coincide. It is known that for m larger than a critical value m* similar or equal to (13.607)(-1) a self-adjoint and lower bounded Hamiltonian H-0 can be constructed, whose domain is characterized in terms of the standard point-interaction boundary condition at each coincidence plane. Here we prove that for m. (m*, m**), where m** similar or equal to (8.62)(-1), there is a further family of self-adjoint and lower bounded Hamiltonians H-0,H-beta, beta epsilon R, describing the system. Using a quadratic form method, we give a rigorous construction of such Hamiltonians and we show that the elements of their domains satisfy a further boundary condition, characterizing the singular behavior when the positions of all the three particles coincide