Ground-state computation of Bose-Einstein condensates by an imaginary-time quantum lattice Boltzmann scheme.
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.
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Dipartimento di Matematica, Università Roma Tre, Largo San Leonardo Murialdo 1, 00146, Roma, Italy.
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Spigler
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