Algorithmic and software support of theoretical investigations

Numerical investigations methods for quantum systems with many degrees of freedom, based on approximate functional integration approach is elaborated. The thermodynamic characteristics of three-dimensional Bose gas are studied. The computation algorithm of functional integrals appearing in this problem, including particle identification and wave function symmetry principles is created [7]. A numerical method for the inverse problem of quantum scattering theory is suggested. It is based on two asymptotic regulations: the first one uses the asymptotic behaviors of the phase shift and of the Jost function module for high energies, and the second one - the by step asymptotic discretisation of the reciprocals to "almost" Toeplitz and Hankel matrices. The last one permits to avoid the unstable procedure of numerical differentiation [8].

A new quantization condition for asymptotic momenta of decay products of a resonance was obtained [9]. The mathematical statements of boundary Schwinger-Dyson and Bethe-Salpeter problems for some quark potential QCD models and the QCD-inspired quarkonium model at finite temperature are proposed. An algorithm for numerical investigation is constructed and numerical analysis of models is performed [10]. The LLP-equations in bipolaron theory have been solved numerically [11]. The numerical modeling of the dynamics of gas motion with account of active surface has been performed [12]. Algorithms, software and numerical study of some muon catalyzed fusion processes and exotic atoms have been presented on International Symposium mu CF-95, Dubna, 1995. Algorithms and software for computing of quasielastic scattering parameters of some light exotic nuclei are created [13]. Numerical investigation of the resonance phenomena in subatomic physics has been performed [14]. Software and numerical study of the quasiparticle- phonon nuclei model has been done [15].