Differential cross sections have been measured for nucleon-isobar production and elastic scattering in p -p interactions from 6.2 to 29.7 GeV/c in the laboratory angle range 8 < O , ,
associated with phase diffusion brought about by a random noise perturbation due to thermal fluctuations. In the quantum theory, the process of contraction of the density matrix after the decay of each injected atom would convert even a pure case into a mixture, so that Eqs. (2) really describe an ensemble of lasers for which phase information is gradually lost. The density matrix does not describe the laser but rather our state of knowledge of the ensemble of lasers under consideration. If we knew initially that a single laser had a nonvanishing electric field, a density matrix with nonzero off-diagonal elements would be required for the initial description, and the average electric field would only decay with the very long mean life of 1/D.
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