DECOHERENCE AND DEPHASING IN A QUANTUM MEASUREMENT PROCESS

We numerically simulate the quantum measurement process by modeling th e measuring apparatus as a one-dimensional Dirac comb that interacts w ith an incoming object particle. The global effect of the apparatus ca n be well schematized in terms of the total transmission probability a nd the decoherence parameter, which quantitatively characterizes the l oss of quantum-mechanical coherence and the wave-function collapse by measurement. These two quantities alone enable one to judge whether th e apparatus works well or not as a detection system. We derive simple theoretical formulas that are in excellent agreement with the numerica l results, and can be very useful in order to make a ''design theory'' of a measuring system (detector). We also discuss some important char acteristics of the wave-function collapse.