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arXiv:quant-ph/9712022

Three Body Multichannel Scattering as a Model of Irreversible Quantum Mechanics

А. В. Богданов, Ashot S. Gevorkyan

Published Dec 10, 1997• 7 citations
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Abstract

The new formulation of the theory of multichannel scattering on the example of collinear model is proposed. It is shown, that in the closed three-body scattering system the principle of quantum determinism in general case breaks down and we have a micro- irreversible quantum mechanics.
DOI
10.48550/arxiv.quant-ph/9712022

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A new micro-irreversible 3D theory of quantum multichannel scattering in the three-body system is developed. The quantum approach is constructed on the generating trajectory tubes which allow taking into account influence of classical non-integrability on the dynamical quantum system. It was shown that when the volume of classical chaos in phase space is larger than quantum sell in the main object of quantum system the wavefunction generates chaos (quantum chaos). The probability of quantum transitions is constructed for this case. On the example of collinear collision of Li+(FH) -> (LiF)+H system is carried out the numerical calculation and was shown that in the system is generated quantum (wave) chaos.
Abstract In the preceding chapters we have given a detailed discussion of quaternionic scattering theory for the case of a single particle incident on a fixed external scattering potential. In complex quantum mechanics the external potential problem is of course only an idealized model, obtained from the physically more realistic case of multiparticle scattering when all particles except the incoming projectile are very heavy, or, in the case of the space-translationinvariant two-body problem, as the exact formulation of the internal motion after separation of the center of mass motion.
Derivations are given for some transition and resolvent operator equations for multichannel quantum scattering with short-range potentials. The basic difference between these and previous equations is that the unknown operators act only on the channel subspaces. This is made possible by utilizing, and extending, the two-Hilbert-space formulation previously given by the authors [in J. Math. Phys. 14, 1328 (1973)]. The equations in abstract form are of the Lippmann–Schwinger type, differing only in the appearance of certain injection operators from one Hilbert space to the other. When applied to multichannel quantum scattering, the abstract theory yields a new system of equations for the transition and resolvent operators. Uniqueness of the solution to the equations is proved.
An approach is developed, combining the ideas of quantum statistical mechanics and multichannel theory of scattering, for treating statistical systems whose constituents can possess different bound states realized as compact clusters. The main principles for constructing multichannel cluster Hamiltonians are formulated: principle of statistical correctness, principle of cluster coexistence, and principle of potential scaling. The importance of the principle of statistical correctness is emphasized by showing that when it does not hold the behaviour of thermodynamic functions becomes essentially distorted. And moreover, unphysical instabilities can appear. The ideas are carefully illustrated by a statistical model of hot nuclear matter.