Particle Tracks, Events and Quantum Theory

The law of track formation in cloud chambers is derived from the Liouvilleequation with a simple Lindblad's type generator that describes couplingbetween a quantum particle and a classical, continuous, medium of two--statedetectors. Piecewise deterministic random process (PDP) corresponding to theLiouville equation is derived. The process consists of pairs (classicalevent,quantum jump), interspersed with random periods of continuous (ingeneral, non--linear) Schroedinger's--type evolution. The classical events areflips of the detectors -- they account for tracks. Quantum jumps are shown, inthe simplest, homogeneous case, to be identical to those in the earlyspontaneous localization model of Ghirardi, Rimini and Weber (GRW). The methodsand results of the present paper allow for an elementary derivation andnumerical simulation of particle track formation and provide an additionalperspective on GRW's proposalComment: 22 page