Unitary quantum lattice gas algorithm generated from the Dirac collision operator for 1D soliton–soliton collisions

A new unitary quantum lattice gas (QLG) algorithm is proposed as a mesoscopic unitary perturbative representation of the mean field Gross Pitaevskii equation for Bose-Einstein Condensates (BECs). This consists of an interleaved sequence of unitary collide-stream operators and is tested on the 1D nonlinear Schrodinger (NLS) equation since exact soliton solutions are well known. An earlier QLG algorithm, based on the [GRAPHICS] collision operator has been found to have limited application to spinor-BECs. Here, a new unitary collision operator, based on the recent QLG of Yepez for the Dirac particle, is used to model the 1D NLS soliton-soliton problem. It is found that this new unitary algorithm can handle parameters (soliton amplitudes and speeds) a factor of over 20 greater than those under the previous [GRAPHICS] algorithm.[Re: (v.07) To be submitted to special issue 'Plasma and Fluid Dynamics: Computational, Experimental and Theoretical Advancement']