The law of track formation in cloud chambers is derived from the Liouville
equation with a simple Lindblad's type generator that describes coupling
between a quantum particle and a classical, continuous, medium of two--state
detectors. Piecewise deterministic random process (PDP) corresponding to the
Liouville equation is derived. The process consists of pairs (classical
event,quantum jump), interspersed with random periods of continuous (in
general, non--linear) Schroedinger's--type evolution. The classical events are
flips of the detectors -- they account for tracks. Quantum jumps are shown, in
the simplest, homogeneous case, to be identical to those in the early
spontaneous localization model of Ghirardi, Rimini and Weber (GRW). The methods
and results of the present paper allow for an elementary derivation and
numerical simulation of particle track formation and provide an additional
perspective on GRW's proposalComment: 22 page
