The multidimensional formulation of the quantum lattice Boltzmann (qLB) scheme is extended to the case of nonlinear quantum wave equations. More specifically, imaginary-time formulations of the qLB scheme are developed and applied to the numerical computation of the ground state of the Gross-Pitaevskii equation in one and two spatial dimensions. The calculation is validated through detailed comparison with other numerical methods, as well as with analytical results based on the Thomas-Fermi approximation. The linear scaling of the time-step size with the spatial mesh spacing, a distinctive feature of the present quantum kinetic approach, is also numerically demonstrated.

Palpacelli, S., Succi, S., Spigler, R. (2007). Ground-state computation of Bose-Einstein condensates by an imaginary-time quantum lattice Boltzmann scheme. PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS, 76, 036712-1-036712-17.

Ground-state computation of Bose-Einstein condensates by an imaginary-time quantum lattice Boltzmann scheme

SPIGLER, Renato
2007-01-01

Abstract

The multidimensional formulation of the quantum lattice Boltzmann (qLB) scheme is extended to the case of nonlinear quantum wave equations. More specifically, imaginary-time formulations of the qLB scheme are developed and applied to the numerical computation of the ground state of the Gross-Pitaevskii equation in one and two spatial dimensions. The calculation is validated through detailed comparison with other numerical methods, as well as with analytical results based on the Thomas-Fermi approximation. The linear scaling of the time-step size with the spatial mesh spacing, a distinctive feature of the present quantum kinetic approach, is also numerically demonstrated.
2007
Palpacelli, S., Succi, S., Spigler, R. (2007). Ground-state computation of Bose-Einstein condensates by an imaginary-time quantum lattice Boltzmann scheme. PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS, 76, 036712-1-036712-17.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/150138
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