Quantum Dynamical Approach of Wavefunction Collapse in Measurement Process and Its Application to Quantum Zeno Effect

Abstract

The systematical studies on the dynamical approach of wavefunction collapse in quantum measurement are report in this paper based on the Hepp-Coleman's model and its generalizations. Under certain physically reasonable conditions, which are easily satisfied by the practical problems, it is shown that the off-diagonal elements of the reduced density matrix for the measured system vanish in quantum mechanical evolution process of the universe formed by the measured system plus the measuring instrument-detector at the macroscopic limit with a very large particle number N. Various examples with detector made up of oscillators of different spectrum distribution are used to illustrate this observations. With the two-level system as an explicit illustration, the quantum information entropy is exactly obtained to quantitatively describe the degree of decoherence for the so-called partial coherence caused by detector. The entropy for the case with many levels is computed based on perturbation method in the limits with very large and very small N. As an application of this general approach for quantum measurement, a dynamical realization of the quantum Zeno effect are present to analyse its recent testing experiment in connection with a description of transition in quantum information entropy. Finally, the Cini's model for the correlation between the states of the measured system and the detector is generalized for the case with many energy-level. It is shown that this generalization can also be invoked to give the dynamical realization of wavefunction collapse.