Commun. Comput. Phys.,
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Volume 4.


The Quantum Lattice Boltzmann Equation: Recent Developments

Silvia Palpacelli 1*, Sauro Succi 2

1 Dipartimento di Matematica, Universita Roma Tre, Largo San Leonardo Murialdo 1, 00146, Roma, Italy.
2 Istituto Applicazioni del Calcolo, Viale Policlinico 137, 00161 Roma, Italy.

Received 26 February 2008; Accepted (in revised version) 25 June 2008
Available online 8 July 2008

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 Schrodinger 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.


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PACS: 02.70.-c, 03.65-w, 03.67.Lx
Key words: Quantum lattice Boltzmann, multi-dimensions, imaginary-time model, linear and non-linear Schrodinger equation, adiabatic limit.

*Corresponding author.
Email: palpacel@mat.uniroma3.it (S. Palpacelli), succi@iac.rm.cnr.it (S. Succi)
 

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