Isotropy of three-dimensional quantum lattice Boltzmann schemes

被引：24

作者：

Dellar, P. J. ^{[1
]}

Lapitski, D. ^{[1
]}

Palpacelli, S. ^{[2
]}

Succi, S. ^{[3
]}

机构：

[1] Math Inst, OCIAM, Oxford OX1 3LB, England

[2] Numidia Soc Responsabilita Limitata, I-00144 Rome, Italy

[3] CNR, Ist Appl Calcolo, I-00185 Rome, Italy

来源：

PHYSICAL REVIEW E | 2011年 / 83卷 / 04期

基金：

英国工程与自然科学研究理事会;

关键词：

SCHRODINGER-EQUATION; CELLULAR-AUTOMATA; GAS AUTOMATA; DIRAC; MODEL;

D O I：

10.1103/PhysRevE.83.046706

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

Numerical simulations with previous formulations of the quantum lattice Boltzmann (QLB) scheme in three spatial dimensions showed significant lack of isotropy. In two or more spatial dimensions the QLB approach relies upon operator splitting to decompose the time evolution into a sequence of applications of the one-dimensional QLB scheme along coordinate axes. Each application must be accompanied by a rotation of the wave function into a basis of chiral eigenstates aligned along the relevant axis. The previously observed lack of isotropy was due to an inconsistency in the application of these rotations. Once this inconsistency is removed, the QLB scheme is shown to exhibit isotropic behavior to within a numerical error that scales approximately linearly with the lattice spacing. This establishes the viability of the QLB approach in two and three spatial dimensions.

引用

页数：9

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