A Quantum Stochastic Model for the Track in the Cloud Chamber

By making use of the formalism of Non-Equilibrium Thermo Field Dynamics (NETFD)*, we revealed that there are, in the Langevin equation, infinite options of martingale operators, Hermitian or non-Hermitian, which provide us with a unique quantum master equation.In order to understand physical meaning of the existence of these options, we will study dynamically the problem why the track of an injected particle in the cloud chamber keeps its width finite with the help of the system of stochastic differential equations within NETFD.It will be shown that the watch-dog effect, i.e., the continuous on-demolition measurement of the injected particle by the gas molecules, prevents the wave packet spreading out in contrast with the case of a free particle.Through this application, we will see that the options of martingales may correspond to those of possible measurement procedures.

* NETFD is a canonical operator formalism of quantum systems in far-from-equilibrium state which enables us to treat dissipative quantum systems by a method similar to the usual quantum field theory that accommodates the concept of the dual structure in the interpretation of nature, i.e. in terms of the operator algebra and the representation space.