Discrete Time Leads to Quantum-Like Interference of Deterministic   Particles
  In this note we demonstrate that a quantum-like interference picture could appear as a statistical effect of interference of deterministic particles, i.e. particles that have trajectories and obey deterministic equations, if one introduces a discrete time. The nature of the resulting interference picture does not follow from the geometry of force field, but is strongly attached to the time discreetness parameter. As a demonstration of this concept we consider a scattering of charged particles on the charged screen with a single slit. The resulting interference picture has a nontrivial minimum-maximum distribution which vanishes as the time discreetness parameter goes to zero that could be interpreted as an analog of quantum decoherence. 
Andrei Khrennikov and Yaroslav Volovich