Foundations of Physics

, Volume 8, Issue 9–10, pp 735–744 | Cite as

Self-turbulence in the motion of a free particle

  • G. Sivashinsky


A deterministic equation of the Hamilton-Jacobi type is proposed for a single particle:St+(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.


Energy Level Single Particle Uncertainty Relation Free Particle Classical Trajectory 
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Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • G. Sivashinsky
    • 1
  1. 1.Department of Mathematical Sciences, Division of Applied MathematicsTel-Aviv UniversityRamat-Aviv, Tel-AvivIsrael

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