Berggren Karl-Fredrik, Maksimov Dmitrii N, Sadreev Almas F, Höhmann Ruven, Kuhl Ulrich, Stöckmann Hans-Jürgen
IFM-Theory and Modeling, Linköping University, S-581 83 Linköping, Sweden.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jun;77(6 Pt 2):066209. doi: 10.1103/PhysRevE.77.066209. Epub 2008 Jun 12.
This paper reports on a joint theoretical and experimental study of the Pauli quantum-mechanical stress tensor T_{alphabeta}(x,y) for open two-dimensional chaotic billiards. In the case of a finite current flow through the system the interior wave function is expressed as psi=u+iv . With the assumption that u and v are Gaussian random fields we derive analytic expressions for the statistical distributions for the quantum stress tensor components T_{alphabeta} . The Gaussian random field model is tested for a Sinai billiard with two opposite leads by analyzing the scattering wave functions obtained numerically from the corresponding Schrödinger equation. Two-dimensional quantum billiards may be emulated from planar microwave analogs. Hence we report on microwave measurements for an open two-dimensional cavity and how the quantum stress tensor analog is extracted from the recorded electric field. The agreement with the theoretical predictions for the distributions for T_{alphabeta}(x,y) is quite satisfactory for small net currents. However, a distinct difference between experiments and theory is observed at higher net flow, which could be explained using a Gaussian random field, where the net current was taken into account by an additional plane wave with a preferential direction and amplitude.
本文报道了关于开放二维混沌台球的泡利量子力学应力张量(T_{αβ}(x,y))的理论与实验联合研究。在有限电流通过系统的情况下，内部波函数表示为(\psi = u + iv)。假设(u)和(v)是高斯随机场，我们推导出了量子应力张量分量(T_{αβ})统计分布的解析表达式。通过分析从相应薛定谔方程数值获得的散射波函数，对具有两个相对引线的 Sinai 台球测试了高斯随机场模型。二维量子台球可以从平面微波模拟中进行仿真。因此，我们报告了对开放二维腔的微波测量，以及如何从记录的电场中提取量子应力张量类似物。对于小净电流，(T_{αβ}(x,y))分布的理论预测与实验结果相当吻合。然而，在较高净流量下观察到实验与理论之间存在明显差异，这可以用高斯随机场来解释，其中净电流由具有优先方向和幅度的附加平面波来考虑。
