Palpacelli S, Succi S, Spigler R
Dipartimento di Matematica, Università Roma Tre, Largo San Leonardo Murialdo 1, 00146, Roma, Italy.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Sep;76(3 Pt 2):036712. doi: 10.1103/PhysRevE.76.036712. Epub 2007 Sep 28.
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.
量子晶格玻尔兹曼（qLB）方案的多维公式被扩展到非线性量子波动方程的情形。更具体地说，开发了qLB方案的虚时公式，并将其应用于一维和二维格罗斯 - 皮塔耶夫斯基方程基态的数值计算。通过与其他数值方法以及基于托马斯 - 费米近似的解析结果进行详细比较，验证了计算结果。还通过数值证明了时间步长与空间网格间距的线性缩放关系，这是当前量子动力学方法的一个显著特征。
