2015/06/08 by Yu Gu, Gu, Yu, Lenya Ryzhik +1
Engineering · #Acoustic Wave Phenomena Research #Analysis of PDEs (math.AP) #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Microwave Imaging and Scattering Analysis #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1506.02728
openalex publication_date 2015/06/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We analyze the solutions of the Schrödinger equation with the low frequency initial data and a time-dependent weakly random potential. We prove a homogenization result for the low frequency component of the wave field. We also show that the dynamics generates a non-trivial energy in the high frequencies, which do not homogenize -- the high frequency component of the wave field remains random and the evolution of its energy is described by a kinetic equation. The transition from the homogenization of the low frequencies to the random limit of the high frequencies is illustrated by understanding the size of the small random fluctuations of the low frequency component.