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Published April 1, 1981 | public
Journal Article Open

Mean-field approximation to the many-body S matrix


A nonperturbative method is developed for calculating the excitation of a many-body system by a time-dependent Hamiltonian. The stationary-phase approximation to a functional-integral representation of the interaction-picture many-body evolution operator results in a mean-field approximation to the S matrix which is asymptotically time independent. A one-body temporally nonlocal evolution equation defines the stationary mean-field configurations. The general method and character of the stationary solutions are illustrated by application to the forced harmonic oscillator and forced Lipkin model. Potential applications to realistic nuclear and atomic scattering situations are discussed.

Additional Information

©1981 The American Physical Society Received 1 July 1980 We are grateful for conversations with Dr. K.R. Sandhya Devi and George Fuller during the early stages of this work. Discussions with Dr. Shimon Levit have also been very useful. Y. Alhassid is a Chaim Weizmann Post-doctoral Fellow and S. Koonin holds an Alfred P. Sloan Foundation research fellowship. This work was supported in part by the National Science Foundation under Contract Nos. PHY77-21602 and PHY79-23638.


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