Shock Waves in Bose-Einstein Condensation Under Gaussian White Noise

Abstract

We investigate the Gross-Pitaevskii equation with the tilted bichromatical optical lattice potential for finding the dynamics of a Bose-Einstein condensate system under the Gaussian white noise. We construct the Poincare sections of system based on the relations between the system parameters and solution behaviors to understand how its shock wave like dynamic could be affected by the noise. Also the hierarchical cluster analysis method investigation of the system is presented.