Tuesday, April 11, 2023
MLIT Room 310
1. A.A. Gusev, G. Chuluunbaatar, O. Chuluunbaatar, S.I. Vinitsky

Construction and application of fully symmetric quadrature rules on the simplexes

Speaker: A.A. Gusev
A method for constructing fully symmetric quadrature rules of Gaussian type with positive weights, and with nodes lying inside the simplex is discussed. The quadrature rules up to 20-th order on the tetrahedron, 16-th order on 4-simplex, 10-th order on 5- and 6-simplexes are obtained. For the convenience of their use, the INQSIM program was created and presented in the JINR program library (JINRLIB). The developed method is oriented on solving the six-dimensional elliptic boundary value problem by the finite element method for describing the discrete spectrum of the collective model of the atomic nucleus.
2. A. Khvedelidze, A. Torosyan

Describing classicality of states of a finite-dimensional quantum system via Wigner function positivity

Speaker: A. Torosyan
In the present report, within the phase-space formulation of quantum theory of N - level quantum system, three measures of classicality constructed out of the quasiprobability distributions will be discussed. All considered measures are based on the existence of the "classical states" defined as those whose Wigner function is positive semi-definite over the whole phase space. The variety of classicality measures originates from different ways of quantifying deviations of states from the subset of classical states. Algebraic and geometric descriptions of the set of classical states will be given in terms of the corresponding convex bodies located inside the simplex of density matrices eigenvalues. A few computational aspects of classicality measures will be discussed and exemplified for qubits, qutrits and quatrits.
3. V.V. Kornyak

Constructive versions of quantum mechanics

Modern problems of quantum physics and quantum informatics require a detailed analysis of the "fine structure" of quantum systems, which cannot be carried out using traditional approximate methods of standard quantum mechanics. Therefore, the development of accurate constructive approaches to the study of quantum systems seems to be an actual task. The talk considers a modification of quantum mechanics based on permutation representations of finite groups in Hilbert spaces over cyclotomic fields, and discusses its connection with the "finite quantum mechanics" of Weyl-Schwinger.