Impulsive quantum measurements: restricted path integral versus von Neumann collapse

The relation between the restricted path integral approach to quantum measurement theory and the commonly accepted von Neumann wavefunction collapse postulate is presented. It is argued that in the limit of impulsive measurements the two approaches lead to the same predictions. The example of repeated impulsive quantum measurements of position performed on a harmonic oscillator is discussed in detail and the quantum nondemolition strategies are recovered in both the approaches.Comment: 12 pages, 3 figure

Dynamics of Quantum Collapse in Energy Measurements

The influence of continuous measurements of energy with a finite accuracy is studied in various quantum systems through a restriction of the Feynman path-integrals around the measurement result. The method, which is equivalent to consider an effective Schr\"odinger equation with a non-Hermitian Hamiltonian, allows one to study the dynamics of the wavefunction collapse. A numerical algorithm for solving the effective Schr\"odinger equation is developed and checked in the case of a harmonic oscillator. The situations, of physical interest, of a two-level system and of a metastable quantum-well are then discussed. In the first case the Zeno inhibition observed in quantum optics experiments is recovered and extended to nonresonant transitions, in the second one we propose to observe inhibition of spontaneous decay in mesoscopic heterostructures. In all the considered examples the effect of the continuous measurement of energy is a freezing of the evolution of the system proportional to the accuracy of the measurement itself.Comment: 20 pages with figures, compressed and uuencoded ps fil