Bettelheim E, Abanov Alexander G, Wiegmann P
James Frank Institute, University of Chicago, 5640 S. Ellis Avenue, Chicago, Illinois 60637, USA.
Phys Rev Lett. 2006 Dec 15;97(24):246401. doi: 10.1103/PhysRevLett.97.246401.
Using the Calogero model as an example, we show that the transport in interacting nondissipative electronic systems is essentially nonlinear and unstable. Nonlinear effects are due to the curvature of the electronic spectrum near the Fermi energy. As is typical for nonlinear systems, a propagating semiclassical wave packet develops a shock wave at a finite time. A wave packet collapses into oscillatory features which further evolve into regularly structured localized pulses carrying a fractionally quantized charge. The Calogero model can be used to describe fractional quantum Hall edge states. We discuss perspectives of observation of quantum shock waves and a direct measurement of the fractional charge in fractional quantum Hall edge states.
以卡洛杰罗模型为例，我们表明，在相互作用的无耗散电子系统中的输运本质上是非线性且不稳定的。非线性效应源于费米能量附近电子能谱的曲率。正如非线性系统的典型情况那样，一个传播的半经典波包在有限时间内会形成一个冲击波。一个波包坍缩成振荡特征，这些振荡特征进一步演变成携带分数量化电荷的规则结构化局域脉冲。卡洛杰罗模型可用于描述分数量子霍尔边缘态。我们讨论了观测量子冲击波以及直接测量分数量子霍尔边缘态中的分数电荷的前景。
