The Analogue of Bohm-Bell Processes on a Graph

Abstract

Bohm-Bell processes, of interest in the foundations of quantum field theory, form a class of Markov processes $Q_t$ 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 $Q_t$ is $|{\psi }_t{|}^2$ with $\psi$ 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.

15 pages LaTeX, 1 figure; v2 minor corrections

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Cited by in corpus (5)

• The "Unromantic Pictures" of Quantum Theory
• On the stochastic Allen-Cahn equation on networks with multiplicative noise
• Diffusion processes in thin tubes and their limits on graphs
• Enhanced quantum transport in chiral quantum walks
• Stochastic reaction-diffusion equations on networks with dynamic time-delayed boundary conditions