TY - JOUR T1 - The Quantum Lattice Boltzmann Equation: Recent Developments AU - Silvia Palpacelli & Sauro Succi JO - Communications in Computational Physics VL - 5 SP - 980 EP - 1007 PY - 2008 DA - 2008/11 SN - 4 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7823.html KW - AB -

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.