Weyl asymptotics: From closed to open systems

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 86, Issue 6, 2012, Pages

  Potzuweit, A ^a   Weich, T ^a   Barkhofen, S ^a   Kuhl, U ^a,b   Stockmann H J ^a   Zworski, M ^c  

^a PHILIPPS UNIVERSITY MARBURG   (Germany)

^b UNIVERSITÉ CÔTE D'AZUR   (France)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTICS; CLOSED SYSTEMS; COUNTING FUNCTIONS; HARMONIC INVERSIONS; MICROWAVE EXPERIMENTS; MICROWAVE REFLECTION;

RESONANCE;

OPEN SYSTEMS;

EID: 84871464408     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.86.066205     Document Type: Article

References (58)

1. H. Weyl, J. Reine Angew. Math. 0075-4102 10.1515/crll.1912.141.163 1912, 163 (2009).
2. J. H. Jeans, Philos. Mag. V10, 91 (1905).
3. L. Hörmander, Acta Math. ACMAA8 0001-5962 10.1007/BF02391913 121, 193 (1968).
4. J. J. Duistermaat and V. W. Guillemin, Invent. Math. INVMBH 0020-9910 10.1007/BF01405172 29, 39 (1975).
5. V. J. Ivri, Funct. Anal. Appl. FAAPBZ 0016-2663 10.1007/BF01086550 14, 98 (1980).
6. V. J. Ivri, Funct. Anal. Appl. FAAPBZ 0016-2663 10.1007/BF01081624 16, 101 (1982).
7. R. Balian and C. Bloch, Ann. Phys. (NY) APNYA6 0003-4916 10.1016/0003-4916(70)90497-5 60, 401 (1970).
8. S. Deus, P. M. Koch, and L. Sirko, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.52.1146 52, 1146 (1995).
9. H.-D. Gräf, H. L. Harney, H. Lengeler, C. H. Lewenkopf, C. Rangacharyulu, A. Richter, P. Schardt, and H. A. Weidenmüller, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.69.1296 69, 1296 (1992).
10. M. Sieber, U. Smilansky, S. C. Creagh, and R. G. Littlejohn, J. Phys. A 1361-6447 10.1088/0305-4470/26/22/022 26, 6217 (1993).
11. M. V. Berry, Distribution of Modes in Fractals Resonators (Springer, Berlin, Heidelberg, New York, 1979), p. 51.
12. J. Brossard and R. Carmona, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01210795 104, 103 (1986).
13. R. E. Prange, E. Ott, T. M. Antonsen, Jr., B. Georgeot, and R. Blümel, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.53.207 53, 207 (1996).
14. P. Gaspard and S. A. Rice, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.456018 90, 2242 (1989).
15. W. John, B. Milek, H. Schanz, and P. Zeba, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.67.1949 67, 1949 (1991).
16. F. Haake, F. Izrailev, N. Lehmann, D. Saher, and H.-J. Sommers, Z. Phys. B ZPCMDN 0722-3277 10.1007/BF01470925 88, 359 (1992).
17. C. Poli, G. A. Luna-Acosta, and H.-J. Stöckmann, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.108.174101 108, 174101 (2012).
18. J. Okolowicz, M. Ploszajczak, and I. Rotter, Phys. Rep. 0370-1573 10.1016/S0370-1573(02)00366-6 374, 271 (2003).
19. I. Rotter, J. Phys. A 1751-8113 10.1088/1751-8113/42/15/153001 42, 153001 (2009).
20. E. Persson, I. Rotter, H.-J. Stöckmann, and M. Barth, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.2478 85, 2478 (2000).
21. W. Lu, M. Rose, K. Pance, and S. Sridhar, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.5233 82, 5233 (1999).
22. J. Sjöstrand, Duke Math. J. DUMJAO 0012-7094 10.1215/S0012-7094-90- 06001-6 60, 1 (1990).
23. K. K. Lin, J. Comp. Phys. JCTPAH 0021-9991 10.1006/jcph.2001.6986 176, 295 (2002).
24. W. T. Lu, S. Sridhar, and M. Zworski, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.154101 91, 154101 (2003).
25. M. Zworski, Invent. Math. INVMBH 0020-9910 10.1007/s002220050313 136, 353 (1999).
26. L. Guillopé, K. K. Lin, and M. Zworski, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/s00220-003-1007-1 245, 149 (2004). (Pubitemid 38341540)
27. H. Schomerus and J. Tworzydło, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.154102 93, 154102 (2004).
28. S. Nonnenmacher and M. Zworski, J. Phys. A 1361-6447 10.1088/0305-4470/ 38/49/014 38, 10683 (2005). (Pubitemid 41706112)
29. J. P. Keating, M. Novaes, S. D. Prado, and M. Sieber, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.150406 97, 150406 (2006). (Pubitemid 44570411)
30. J. Sjöstrand and M. Zworski, Duke Math. J. DUMJAO 0012-7094 10.1215/S0012-7094-07-13731-1 137, 381 (2007).
31. M. Kopp and H. Schomerus, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.81.026208 81, 026208 (2010).
32. L. Ermann and D. L. Shepelyansky, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2010-00144-0 75, 299 (2010).
33. L. Ermann, A. D. Chepelianskii, and D. L. Shepelyansky, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2010-10774-7 79, 115 (2011).
34. A. Eberspächer, J. Main, and G. Wunner, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.82.046201 82, 046201 (2010).
35. J. M. Pedrosa, G. G. Carlo, D. A. Wisniacki, and L. Ermann, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.79.016215 79, 016215 (2009).
36. J. M. Pedrosa, D. Wisniacki, G. G. Carlo, and M. Novaes, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.85.036203 85, 036203 (2012).
37. J. A. Ramilowski, S. D. Prado, F. Borondo, and D. Farrelly, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.80.055201 80, 055201(R) (2009).
38. J. Strain and M. Zworski, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/17/5/003 17, 1607 (2004). (Pubitemid 39289012)
39. J. Wiersig and J. Main, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.77.036205 77, 036205 (2008). (Pubitemid 351415922)
40. H. Schomerus, J. Wiersig, and J. Main, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.053806 79, 053806 (2009).
41. H. Christianson, Canad. J. Math. CJMAAB 0008-414X 10.4153/CJM-2007-013-4 59, 311 (2007).
42. S. Nonnenmacher, J. Sjöstrand, and M. Zworski, arXiv: 1105.3128 v1 [Ann. Math. (to be published)].
43. K. Datchev and S. Dyatlov, arXiv: 1206.2255 v3.
44. M. Ikawa, Ann. Inst. Fourier AIFUA7 0373-0956 10.5802/aif.1137 38, 113 (1988).
45. P. Gaspard and S. A. Rice, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.456017 90, 2225 (1989).
46. P. Cvitanović and B. Eckhardt, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.63.823 63, 823 (1989).
47. K. Pance, W. Lu, and S. Sridhar, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.2737 85, 2737 (2000).
48. W. Lu, L. Viola, K. Pance, M. Rose, and S. Sridhar, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.61.3652 61, 3652 (2000).
49. H.-J. Stöckmann, Quantum Chaos-An Introduction (Cambridge University Press, Cambridge, 1999).
50. H. P. Baltes and E. R. Hilf, Spectra of Finite Systems (BI-Wissenschaftsverlag, Mannheim, 1976).
51. H.-J. Stöckmann, E. Persson, Y.-H. Kim, M. Barth, U. Kuhl, and I. Rotter, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.65.066211 65, 066211 (2002). (Pubitemid 40606671)
52. J. Ginibre, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1704292 6, 440 (1965).
53. F. Haake, Quantum Signatures of Chaos, 2nd ed. (Springer, Berlin, 2001).
54. L. Ermann, G. G. Carlo, and M. Saraceno, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.054102 103, 054102 (2009).
55. J. Stein, H.-J. Stöckmann, and U. Stoffregen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.75.53 75, 53 (1995).
56. J. Main, P. A. Dando, D. Belkić, and H. S. Taylor, J. Phys. A 1361-6447 10.1088/0305-4470/33/6/311 33, 1247 (2000).
57. U. Kuhl, R. Höhmann, J. Main, and H.-J. Stöckmann, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.254101 100, 254101 (2008).
58. H. Padé, Sur la Représentation Approchée d'une Fonction par des Fractions Rationnelles, théses de la Faculté des sciences de Paris No. 740 (Gauthier-Villars et Fils, Paris, France, 1892).