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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.