Semiclassical expectation values by adiabatic switching: Trapping and tunneling in the chaotic regime

The adiabatic switching technique is adapted to the calculation of expectation values for chaotic systems. Semiclassical results obtained in this manner are compared to accurate quantum expectation values for the Hénon-Heiles system at high energy. Although good agreement is found for most states, the incidence of discrepancies grows as the energy increases. Almost all such discrepancies can be attributed to either quantum trapping effects for states with extreme values of quantum numbers or tunneling effects associated with the avoided crossings of energy curves as a function of a parameter in the Hamiltonian. As the energy is raised and the system becomes more chaotic, the increased strength of the avoided crossings leads to more frequent and stronger tunneling. The possible generality of this result and its implications for statistical quantum behavior are discussed.