Brownian motion with the exposure time control
D. Sokolovski · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 1996
We solve a classical analog of the quantum traversal time problem. The classical diffusion equation is modified to control the amount of time spent by a particle in a specified region of space. The ``clocked'' diffusion equation is solved for an ensemble of Brownian particles confined in a closed volume. Long term behavior of the exposure time distribution is analyzed. A general recipe for including time control into fieldlike equations of motion describing evolution of a physical system is proposed. \textcopyright{} 1996 The American Physical Society.