Abstract
Based on an analysis of Feynman's path integral formulation of the propagator, a relative criterion is proposed for validity of a semiclassical approach to the dynamics near critical points in a class of systems undergoing quantum phase transitions. It is given by an effective Planck constant, in the relative sense that a smaller effective Planck constant implies better performance of the semiclassical approach. Numerical tests of this relative criterion are given in the XY model and in the Dicke model.
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