#### Title:

On Construction of Probability Currents BetweenAsymptotic Subspaces of Multichannel Scattering

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#### Uncontrolled Keywords:

Classical three-body problem ; Riemannian space ; irreversibly system ; stochastic equations ; probability current

#### Abstract:

In this paper we prove: The general three-body problem formulated on Riemannian geometry makes it possible to discover new hidden symmetries of the internal motion of a dynamical system and reduce the problem to the system of order 6 th. It is shown that the equivalence of the initial Newtonian three-body problem and developed representation provides coordinate transformations in combination with an underdefinished system of algebraic equations. The latter makes a system of geodesic equations relative to the evolution parameter, i.e., the arc length of the geodesic curve, irreversible. To describe the motion of a dynamical system influenced by external regular and stochastic forces, a system of stochastic equations (SDE) is obtained. Using the system of SDE, a partial differential equation of the second order for the joint probability distribution of the momentum and coordinate of dynamical system in the phase space is obtained. A criterion for estimating the degree of deviation of probabilistic current tubes of geodesic trajectories in the phase and configuration spaces is formulated. The mathematical expectation of the transition probability between two asymptotic channels is determined, taking into account the multichannel character of the scattering.

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#### Affiliation:

Institute for Informatics and Automation Problems ; Institute of Chemical Physics

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#### Conference title:

11th International Conference on Computer Science and Information Technologies CSIT 2017