The Analogue of Bohm–Bell Processes on a Graph

Bohm–Bell processes, of interest in the foundations of quantum field theory, form a class of Markov processes Qt generalizing in a natural way both Bohm’s dynamical system in configuration space for nonrelativistic quantum mechanics and Bell’s jump process for lattice quantum field theories. They are such that at any time t the distribution of Qt is |ψt| 2 with ψ the wave function of quantum theory. We extend this class here by introducing the analogous Markov process for quantum mechanics on a graph (also called a network, i.e., a space consisting of line segments glued together at their ends). It is a piecewise deterministic process whose innovations occur only when it passes through a vertex. MSC (2000): 81S99, 60J25. PACS: 02.50.Ga; 03.65.Ta.