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摘要
For the solution u(t) to the discrete Schrodinger equation i d/dt u(n)(t) = - (u(n+1)(t) + u(n-1)(t)) + V(theta + n alpha)u(n)(t), n is an element of Z, with alpha is an element of R\Q and V is an element of C-omega(T, R), we consider the growth rate with t of its diffusion norm < u(t)>(p) := (Sigma(n is an element of Z)(n(p) + 1)|u(n)(t)|(2))(1/2), and the (non-averaged) transport exponents beta(+)(u)(p) := lim sup(t ->infinity) 2 log < u(t)>(p)/p log t, beta(-)(u)(p) := lim inf(t ->infinity) 2 log < u(t)>(p)/p log t. We will show that, if the corresponding Schrodinger operator has purely absolutely continuous spectrum, then beta(+/-)(u)(p) = 1, provided that u(0) is well localized.
- 出版日期2017-5
