Non-stochasticity of time-dependent quadratic Hamiltonians and the spectra of canonical transformations. (English) Zbl 0601.70013

The authors consider a classical Hamiltonian which is a quadratic polynomial in q and p with time-dependent coefficients. By assuming that the time dependence of the coefficients is piecewise continuous, the authors prove that the Floquet operator has either a strictly pure point spectrum or has a strictly transient absolutely continuous spectrum. This is supposed to imply that the corresponding quantum mechanical motion is non-stochastic. Further, by considering a simple model of a quadratic Hamiltonian with random time-dependence, the authors show that the corresponding quantum mechanical motion is almost surely non-stochastic.
Reviewer: Ch.Sharma


70H25 Hamilton’s principle
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
70H05 Hamilton’s equations
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