The Quantum Lattice Boltzmann Equation: Recent Developments

Abstract

The derivation of the quantum lattice Boltzmann model is reviewed with special emphasis on recent developments of the model, namely, the extension to a multi-dimensional formulation and the application to the computation of the ground state of the Gross-Pitaevskii equation (GPE). Numerical results for the linear and nonlinear Schrödinger equation and for the ground state solution of the GPE are also presented and validated against analytical results or other classical schemes such as Crank-Nicholson.