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

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

Scattering problem for local perturbations of the free quantum gas

Kondratiev Y, Konstantinov AY, Röckner M, Shchepan'uk GV. Scattering problem for local perturbations of the free quantum gas. COMMUNICATIONS IN MATHEMATICAL PHYSICS. 1999;203(2):421-444.Scattering theory for perturbations of the intrinsic Dirichlet (Laplace-Beltrami) operator H-0 = - div(Gamma) del(Gamma) on L-2(Gamma, pi(z)) i. e. the space of pi(z)-square integrable functions on the configuration space Gamma over R-d, is studied. Here pi(z) denotes Poisson measure with intensity z. We show that for an arbitrary regular non-zero potential V the standard wave operators W+/-(H-0, H-0 + V) do not exist, and propose to consider Dirichlet operators of perturbed Poisson measures instead of potential perturbations of the Hamiltonian H-0. As case studies, cylindric smooth densities and finite volume Gibbs perturbations of the Poisson measure are considered. In these cases the existence of the corresponding wave operators is proved