The quantum lattice Boltzmann equation: recent developments. (English) Zbl 1364.76245

Summary: 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.


76Y05 Quantum hydrodynamics and relativistic hydrodynamics
76M28 Particle methods and lattice-gas methods
35Q40 PDEs in connection with quantum mechanics
35Q55 NLS equations (nonlinear Schrödinger equations)