Asymptotic relaxation of a system of a large number of interacting particles

A model of an open relaxing system of scalar bosons with one state and random interaction, described by a system of linking equations for the moments, is considered in a Markov approximation. It is shown that in the self-consistent field limit the equations for the first moments are equations of the characteristics with respect to the equation for the generating functions of the system. They can be understood as the scalar analog of a quasilinear Schrödinger equation with a purely imaginary Hamiltonian describing non-Hamiltonian dynamics of an open system of randomly interacting quantum particles. By virtue of the assumption made about the nature of the interaction, the equations of the characteristics obtained differ from those presented earlier, where the means are solutions of linearized relaxation equations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 89–92, October, 1988.In conclusion, I am grateful to V. P. Belavkin for formulating the problems and useful discussions.