Barr Aaron, Barr Ariel, Porter Max D, Reichl Linda E
Center for Complex Quantum Systems and Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA.
Chaos. 2017 Oct;27(10):104604. doi: 10.1063/1.5001186.
When the classical dynamics of a particle in a finite two-dimensional billiard undergoes a transition to chaos, the quantum dynamics of the particle also shows manifestations of chaos in the form of scarring of wave functions and changes in energy level spacing distributions. If we "tile" an infinite plane with such billiards, we find that the Bloch states on the lattice undergo avoided crossings, energy level spacing statistics change from Poisson-like to Wigner-like, and energy sheets of the Brillouin zone begin to "mix" as the classical dynamics of the billiard changes from regular to chaotic behavior.
当有限二维台球中粒子的经典动力学向混沌转变时，粒子的量子动力学也会以波函数的疤痕和能级间距分布变化的形式表现出混沌迹象。如果我们用这样的台球“平铺”一个无限平面，我们会发现晶格上的布洛赫态会发生避免交叉，能级间距统计从泊松型变为维格纳型，并且随着台球的经典动力学从规则行为转变为混沌行为，布里渊区的能量面开始“混合”。
