Random Hamiltonian Models and Quantum Prediction Algorithms

Abstract

This paper describes an algorithm for selecting a consistent set within the consistent histories approach to quantum mechanics and investigates its properties. The algorithm select from among the consistent sets formed by projections defined by the Schmidt decomposition by making projections at the earliest possible time. The algorithm unconditionally predicts the possible events in closed quantum systems and ascribes probabilities to these events. A simple random Hamiltonian model is described and the results of applying the algorithm to this model using computer programs are discussed and compared with approximate analytic calculations.