F. Borgonovi et L. Rebuzzini, TRANSLATIONAL INVARIANCE IN THE KICKED HARMONIC-OSCILLATOR, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 52(3), 1995, pp. 2302-2309
Analysis of the quantum kicked harmonic oscillator in the condition of
resonance (omega(0)T=2 pi/q) is approached in this paper. We extend t
he results found in Berman, Rubaev, and Zaslavsky [Nonlinearity 4, 543
(1991)] by relating the translational invariance of the qth power of
the quasienergy operator with the spreading of the mean energy in time
. These results are then confirmed by numerical simulations.