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Energy evolution in time-dependent harmonic oscillator with arbitrary external forcing
The classical Hamiltonian system of time-dependent harmonic oscillator driven
by the arbitrary external time-dependent force is considered. Exact analytical
solution of the corresponding equations of motion is constructed in the
framework of the technique (Robnik M, Romanovski V G, J. Phys. A: Math. Gen.
{\bf 33} (2000) 5093) based on WKB approach. Energy evolution for the ensemble
of uniformly distributed w.r.t. the canonical angle initial conditions on the
initial invariant torus is studied. Exact expressions for the energy moments of
arbitrary order taken at arbitrary time moment are analytically derived.
Corresponding characteristic function is analytically constructed in the form
of infinite series and numerically evaluated for certain values of the system
parameters. Energy distribution function is numerically obtained in some
particular cases. In the limit of small initial ensemble's energy the relevant
formula for the energy distribution function is analytically derived.Comment: 16 pages, 5 figure