Self-turbulence in the motion of a free particle |
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Authors: | G. Sivashinsky |
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Affiliation: | 1. Department of Mathematical Sciences, Division of Applied Mathematics, Tel-Aviv University, Ramat-Aviv, Tel-Aviv, Israel
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Abstract: | A deterministic equation of the Hamilton-Jacobi type is proposed for a single particle:S t+(1/2m)(?S)2+U{S}=0, whereU{S} is a certain operator onS, which has the sense of the potential of the self-generated field of a free particle. Examples are given of potentials that imply instability of uniform rectilinear motion of a free particle and yieldrandom fluctuations of its trajectory. Galilei-invariant turbulence-producing potentials can be constructed using a single universal parameter—Planck's constant. Despite the fact that the classical trajectory concept is retained, the mechanics of the particle then admits quantum-type effects: an uncertainty relation, de Broglie-type waves and their interference, discrete energy levels, and zero-point fluctuations. |
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