Asymptotics of the Solutions of the Random Schrodinger Equation

作者:Bal Guillaume*; Komorowski Tomasz; Ryzhik Lenya
来源:Archive for Rational Mechanics and Analysis, 2011, 200(2): 613-664.
DOI:10.1007/s00205-010-0386-7

摘要

We consider solutions of the Schrodinger equation with a weak time-dependent random potential. It is shown that when the two-point correlation function of the potential is rapidly decaying, then the Fourier transform of the appropriately scaled solution converges point-wise in xi to a stochastic complex Gaussian limit. On the other hand, when the two-point correlation function decays slowly, we show that the limit of where B (kappa) (t, xi) is a fractional Brownian motion.

  • 出版日期2011-5