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arXiv 1202.6568physics.opticsnlin.CD
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微波实验验证混沌介质谐振器的迹线公式

Trace formula for chaotic dielectric resonators tested with microwave experiments

S. Bittner, B. Dietz, R. Dubertrand, J. Isensee, M. Miski-Oglu, A. Richter

摘要:

我们测量了两个体育场形介质微波谐振器的谐振谱,并测试了Bogomolny等人提出的混沌介质谐振器的半经典迹公式[Phys.Rev.E78,056202(2008)]。我们发现实验数据和痕量公式的预测之间有很好的定性一致性。偏差可归因于根据先前实验[Phys. Rev. E 81,066215(2010)]测得的光谱中缺少共振。数值长度谱的研究表明,与迹线公式有良好的定性和定量一致性。然而,它表明需要对迹线公式进行高阶修正。曲率修正的应用程序的菲涅尔反射系数进入跟踪公式产生了更好的协议,但偏差仍然存在,表明进一步调查的必要性。

英文摘要:

We measured the resonance spectra of two stadium-shaped dielectric microwave resonators and tested a semiclassical trace formula for chaotic dielectric resonators proposed by Bogomolny et al. [Phys. Rev. E 78, 056202 (2008)]. We found good qualitative agreement between the experimental data and the predictions of the trace formula. Deviations could be attributed to missing resonances in the measured spectra in accordance with previous experiments [Phys. Rev. E 81, 066215 (2010)]. The investigation of the numerical length spectrum showed good qualitative and reasonable quantitative agreement with the trace formula. It demonstrated, however, the need for higher-order corrections of the trace formula. The application of a curvature correction to the Fresnel reflection coefficients entering the trace formula yielded better agreement, but deviations remained, indicating the necessity of further investigations.

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