Long time Evolution of Quantum Averages Near Stationary Points

Abstract

We construct explicit expressions for quantum averages in coherent states for a Hamiltonian of degree 4 with a hyperbolic stagnation point. These expressions are valid for all times and "collapse" (i.e., become infinite) along a discrete sequence of times. We compute quantum corrections compared to classical expressions. These corrections become significant over a time period of order C log 1/\hbar.Comment: LaTeX, 8 page