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

引用

页数：8

共 50 条

[1] FROM CLOSED TEACHING TO OPEN LEARNING SYSTEMS
KEEFE, JW
NOTRE DAME JOURNAL OF EDUCATION, 1976, 7 (02): : 168 - 174
[2] The Weyl group and asymptotics: All supergravity billiards have a closed form general integral
Fre, Pietro
Sorin, Alexander S.
NUCLEAR PHYSICS B, 2009, 815 (03) : 430 - 494
[3] PT Symmetry and Weyl Asymptotics
Sjöstrand, Johannes
Springer Proceedings in Mathematics, 2012, 16 : 299 - 308
[4] Weyl asymptotics for Hanoi attractors
Ruiz, Patricia Alonso
Freiberg, Uta R.
FORUM MATHEMATICUM, 2017, 29 (05) : 1003 - 1021
[5] Asymptotics for the Weyl quantized phase
Hennings, M. A.
Smith, T. B.
Dubin, D. A.
1996,
[6] Quantum pumping and dissipation: From closed to open systems
Cohen, D
PHYSICAL REVIEW B, 2003, 68 (20)
[7] Asymptotics for the Weyl quantized phase
Hennings, MA
Smith, TB
Dubin, DA
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1995, 28 (23): : 6779 - 6807
[8] Fractal Weyl laws for chaotic open systems
Lu, WT
Sridhar, S
Zworski, M
PHYSICAL REVIEW LETTERS, 2003, 91 (15)
[9] THE MULTIPLIER IN CLOSED AND OPEN SYSTEMS
Shackle, G. L. S.
OXFORD ECONOMIC PAPERS-NEW SERIES, 1939, 2 (01): : 135 - 144
[10] Bhaskar on open and closed systems
Spurrett, D
SOUTH AFRICAN JOURNAL OF PHILOSOPHY, 2000, 19 (03) : 188 - 208

← 1 2 3 4 5 →