Dynamics of quantum collapse in energy measurements

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Abstract
The influence of continuous measurements of energy with 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 considering an effective Schrödinger equation with a non-Hermitian Hamiltonian, allows one to study the dynamics of the wave-function collapse. A numerical algorithm for solving the effective Schrödinger 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, and in the second case we propose an observation of the 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.