Estimates on Green’s functions, localization and the quantum kicked rotor model

摘要: and phase space L2(1r). It has been conjectured by a number of authors (cf. [FGP], [Bel]) that for typical parameter values a, b, the wave function t satisfying equations (0.1), (0.2) will be almost periodic in time; hence f(t) (the Fourier transform) remains localized. We prove this here, assuming S small. Thus we have: THEOREM. For K stnall (a,b) o?>tside set small rneasure ( > O 0), following holds. Let 4! = W(t, x) solve (0 1), 2) let to 4!(0, suJgciently smooth on T. Then @ is an alrnost timbe, say as Hl(T)-valued map. In particular supt ll@(t)llHl