ASYMPTOTICS OF A TIME-SPLITTING SCHEME FOR THE RANDOM SCHRODINGER EQUATION WITH LONG-RANGE CORRELATIONS

作者：Gomez Christophe^*; Pinaud Olivier

来源：ESAIM: Mathematical Modelling and Numerical Analysis , 2014, 48(2): 411-431.

DOI：10.1051/m2an/2013113

• Random Schrodinger equation
• long-range correlations
• high frequency asymptotics
• splitting scheme

This work is concerned with the asymptotic analysis of a time-splitting scheme for the Schrodinger equation with a random potential having weak amplitude, fast oscillations in time and space, and long-range correlations. Such a problern arises for instance in the simulation of waves propagating in random media in the paraxial approximation. The high-frequency limit of the Schrodinger equation leads to different regimes depending on the distance of propagation, the oscillation pattern of the initial condition, and the statistical properties of the random medium. We show that the splitting scheme captures these regimes in a statistical sense for a time stepsize independent of the frequency.

• 出版日期2014-3