Testing of wave turbulence theory for Gross-Pitaevskii model

Ying Zhu

A famous physical system involved in wave turbulence is Bose-Einstein condensates (BEC), which can be described by the Gross-Pitaevskii equation (GPE). It is also suggested that this model allows statistical motions similar to classical fluid turbulence. An approach known as weak wave turbulence (WWT) theory can be made for GPE, leading to the kinetic equation (KE), which describes the evolution of the spectrum of the turbulent wave field. In this work, we simulate GPE and KE respectively with the same initial field, then we compare the dynamics of them, including statistical spectrum, PDF and cumulants.