Weyl asymptotics: From closed to open systems

被引：27
|
作者：
Potzuweit, A. [1 ]
Weich, T. [1 ,2 ]
Barkhofen, S. [1 ]
Kuhl, U. [1 ,3 ]
Stoeckmann, H. -J. [1 ]
Zworski, M. [4 ]
机构：
[1] Univ Marburg, Fachbereich Phys, D-35032 Marburg, Germany
[2] Univ Marburg, Fachbereich Math, D-35032 Marburg, Germany
[3] Univ Nice Sophia Antipolis, CNRS, Lab Phys Matiere Condensee, UMR 7336, F-06108 Nice, France
[4] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA
来源：
PHYSICAL REVIEW E | 2012年 / 86卷 / 06期
基金：
美国国家科学基金会;
关键词：
ZETA-FUNCTION; STATISTICAL PROPERTIES; QUANTUM RESONANCES; ELLIPTIC-OPERATORS; WAVE-EQUATION; MICROWAVE; DENSITY; DIMENSION; QUANTIZATION; SCATTERING;
D O I：
10.1103/PhysRevE.86.066205
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：
We present microwave experiments on the symmetry reduced five-disk billiard studying the transition from a closed to an open system. The measured microwave reflection signal is analyzed by means of the harmonic inversion and the counting function of the resulting resonances is studied. For the closed system this counting function shows the Weyl asymptotic with a leading exponent equal to 2. By opening the system successively this exponent decreases smoothly to a noninteger value. For the open systems the extraction of resonances by the harmonic inversion becomes more challenging and the arising difficulties are discussed. The results can be interpreted as a first experimental indication for the fractal Weyl conjecture for resonances. DOI: 10.1103/PhysRevE.86.066205
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