Analysis of Missing Level Statistics for Microwave Networks Simulating Quantum Chaotic Graphs Without Time Reversal Symmetry - the Case of Randomly Lost Resonances

• Authors: M. Ławniczak , M. Białous , V. Yunko , S. Bauch , B. Dietz , L. Sirko
• Languages of publication: EN

Abstracts

EN

We present experimental and numerical studies for level statistics in incomplete spectra obtained with microwave networks simulating quantum chaotic graphs with broken time reversal symmetry. We demonstrate that, if resonance frequencies are randomly removed from the spectra, the experimental results for the nearest-neighbor spacing distribution, the spectral rigidity and the average power spectrum are in good agreement with theoretical predictions for incomplete sequences of levels of systems with broken time reversal symmetry.

Keywords

EN

05.40.-a; 05.45.Mt; 05.45.Tp; 03.65.Sq

Discipline

• 05.45.Mt: Quantum chaos; semiclassical methods
• 03.65.Sq: Semiclassical theories and applications
• 05.40.-a: Fluctuation phenomena, random processes, noise, and Brownian motion(for fluctuations in superconductivity, see 74.40.-n; for statistical theory and fluctuations in nuclear reactions, see 24.60.-k; for fluctuations in plasma, see 52.25.Gj; for nonlinear dynamics and chaos, see 05.45.-a)
• 05.45.Tp: Time series analysis

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2017
• Volume: 132
• Issue: 6
• Pages: 1672-1676

Dates

published

2017-12

Contributors

author

M. Ławniczak

• Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland

author

M. Białous

• Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland

author

V. Yunko

• Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland

author

S. Bauch

• Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland

author

B. Dietz

• School of Physical Science and Technology, and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou, Gansu 730000, China

author

L. Sirko

• Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland

References

• [1] J.M.G. Gómez, K. Kar, V.K.B. Kota, R.A. Molina, A. Relaño, J. Retamosa, Phys. Rep. 499, 103 (2011), doi: 10.1016/j.physrep.2010.11.003
• [2] H.A. Weidenmüller, G.E. Mitchell, Rev. Mod. Phys. 81, 539 (2009), doi: 10.1103/RevModPhys.81.539
• [3] F. Haake, Quantum Signatures of Chaos, Springer-Verlag, Heidelberg 2001
• [4] M.L. Mehta, Random Matrices, Academic Press, London 1990
• [5] O. Bohigas, M.J. Giannoni, C. Schmit, Phys. Rev. Lett. 52, 1 (1984), doi: 10.1103/PhysRevLett.52.1
• [6] M.V. Berry, M. Tabor, Proc. R. Soc. A 356, 375 (1977), doi: 10.1098/rspa.1977.0140
• [7] L. Sirko, P.M. Koch, R. Blümel, Phys. Rev. Lett. 78, 2940 (1997), doi: 10.1103/PhysRevLett.78.2940
• [8] H.-J. Stöckmann, Quantum Chaos: An Introduction, Cambridge University Press, Cambridge 2000
• [9] Y. Hlushchuk, A. Błędowski, N. Savytskyy, L. Sirko, Physica Scripta 64, 192 (2001), doi: 10.1238/Physica.Regular.064a00192
• [10] R. Blümel, P.M. Koch, L. Sirko, Found. Phys. 31, 269 (2001), doi: 10.1023/A:1017590503566
• [11] S. Hemmady, X. Zheng, E. Ott, T.M. Antonsen, S.M. Anlage, Phys. Rev. Lett. 94, 014102 (2005), doi: 10.1103/PhysRevLett.94.014102
• [12] B. Dietz, A. Richter, CHAOS 25, 097601 (2015), doi: 10.1063/1.4915527
• [13] M. Ławniczak, M. Białous, V. Yunko, S. Bauch, L. Sirko, Phys. Rev. E 91, 032925 (2015), doi: 10.1103/PhysRevE.91.032925
• [14] B. Dietz, T. Guhr, B. Gutkin, M. Miski-Oglu, A. Richter, Phys. Rev. E 90, 022903 (2014), doi: 10.1103/PhysRevE.90.022903
• [15] T. Kottos, U. Smilansky, Phys. Rev. Lett. 79, 4794 (1997), doi: 10.1103/PhysRevLett.79.4794
• [16] T. Kottos, U. Smilansky, Ann. Phys. 274, 76 (1999), doi: 10.1006/aphy.1999.5904
• [17] P. Pakoński, K. Życzkowski, M. Kuś J. Phys. A 34, 9303 (2001), doi: 10.1088/0305-4470/34/43/313
• [18] O. Hul, S. Bauch, P. Pakoński, N. Savytskyy, K. Życzkowski, L. Sirko, Phys. Rev. E 69, 056205 (2004), doi: 10.1103/PhysRevE.69.056205
• [19] M. Ławniczak, S. Bauch, O. Hul, L. Sirko, Phys. Rev. E 81, 046204 (2010), doi: 10.1103/PhysRevE.81.046204
• [20] M. Ławniczak, S. Bauch, L. Sirko, in Handbook of Applications of Chaos Theory, Eds.: C. Skiadas, C. Skiadas, CRC Press, Boca Raton, USA, 2016, p. 559
• [21] S. Deus, P.M. Koch, L. Sirko, Phys. Rev. E 52, 1146 (1995), doi: 10.1103/PhysRevE.52.1146
• [22] R. Blümel, A. Buchleitner, R. Graham, L. Sirko, U. Smilansky, H. Walther, Phys. Rev. A 44, 4521 (1991), doi: 10.1103/PhysRevA.44.4521
• [23] M. Bellermann, T. Bergemann, A. Haffmann, P.M. Koch, L. Sirko, Phys. Rev. A 46, 5836 (1992), doi: 10.1103/PhysRevA.46.5836
• [24] L. Sirko, S. Yoakum, A. Haffmans, P.M. Koch, Phys. Rev. A 47, R782 (1993), doi: 10.1103/PhysRevA.47.R782
• [25] L. Sirko, P.M. Koch, Appl. Phys. B 60, S195 (1995)
• [26] L. Sirko, A. Haffmans, M.R.W. Bellermann, P.M. Koch, Europhys. Lett. 33, 181 (1996), doi: 10.1209/epl/i1996-00318-5
• [27] L. Sirko, S.A. Zelazny, P.M. Koch, Phys. Rev. Lett. 87, 043002 (2001), doi: 10.1103/PhysRevLett.87.043002
• [28] L. Sirko, P.M. Koch, Phys. Rev. Lett 89, 274101 (2002), doi: 10.1103/PhysRevLett.89.274101
• [29] B. Dietz, T. Friedrich, H.L. Harney, M. Miski-Oglu, A. Richter, F. Schäfer, J. Verbaarschot, H.A. Weidenmüller, Phys. Rev. Lett. 103, 064101 (2009), doi: 10.1103/PhysRevLett.103.064101
• [30] B. Dietz, T. Friedrich, H. L. Harney, M. Miski-Oglu, A. Richter, F. Schäfer, H. A. Weidenmüller, Phys. Rev. E 81, 036205 (2010), doi: 10.1103/PhysRevE.81.036205
• [31] P. So, S.M. Anlage, E. Ott, R. N. Oerter, Phys. Rev. Lett. 74, 2662 (1995), doi: 10.1103/PhysRevLett.74.2662
• [32] U. Stoffregen, J. Stein, H.-J. Stöckmann, M. Kuś, F. Haake, Phys. Rev. Lett. 74, 2666 (1995), doi: 10.1103/PhysRevLett.74.2666
• [33] Dong Ho Wu, Jesse S.A. Bridgewater, A. Gokirmak, S.M. Anlage, Phys. Rev. Lett. 81, 2890 (1998), doi: 10.1103/PhysRevLett.81.2890
• [34] M. Ławniczak, O. Hul, S. Bauch, P. Seba, L. Sirko, Phys. Rev. E 77, 056210 (2008), doi: 10.1103/PhysRevE.77.056210
• [35] M. Ławniczak, S. Bauch, O. Hul, L. Sirko, Phys. Scr. T143, 014014 (2011), doi: 10.1088/0031-8949/2011/T143/014014
• [36] O. Hul, M. Ławniczak, S. Bauch, A. Sawicki, M. Kuś, L. Sirko, Phys. Rev. Lett. 109, 040402 (2012), doi: 10.1103/PhysRevLett.109.040402
• [37] M. Ławniczak, A. Sawicki, S. Bauch, M. Kuś, L. Sirko, Phys. Rev E 89, 032911 (2014), doi: 10.1103/PhysRevE.89.032911
• [38] M. Allgaier, S. Gehler, S. Barkhofen, H.-J. Stöckmann, U. Kuhl, Phys. Rev. E 89, 022925 (2014), doi: 10.1103/PhysRevE.89.022925
• [39] L.J. Pauling, Chem. Phys. 4, 673 (1936)
• [40] J.A. Sanchez-Gil, V. Freilikher, I. Yurkevich, A.A. Maradudin, Phys. Rev. Lett. 80, 948 (1998), doi: 10.1103/PhysRevLett.80.948
• [41] R. Mittra, S.W. Lee, Analytical Techniques in the Theory of Guided Waves, Macmillan, NY 1971
• [42] D. Kowal, U. Sivan, O. Entin-Wohlman, Y. Imry, Phys. Rev. B 42, 9009 (1990), doi: 10.1103/PhysRevB.42.9009
• [43] Y. Imry, Introduction to Mesoscopic Physics Oxford, NY 1996
• [44] S. Gnutzmann, A. Altland, Phys. Rev. Lett. 93, 194101 (2004), doi: 10.1103/PhysRevLett.93.194101
• [45] Z. Pluhař, H. A. Weidenmüller, Phys. Rev. Lett. 112, 144102 (2014), doi: 10.1103/PhysRevLett.112.144102
• [46] O. Bohigas, R.U. Haq, A. Pandey, in Nuclear Data for Science, Technology, Ed. K.H. Böckhoff, Reidel, Dordrecht 1983, doi: 10.1007/978-94-009-7099-1-179
• [47] M. Białous, V. Yunko, S. Bauch, M. Ławniczak, B. Dietz, L. Sirko, Phys. Rev. Lett. 117, 144101 (2016), doi: 10.1103/PhysRevLett.117.144101
• [48] B. Dietz, V. Yunko, M. Białous, S. Bauch, M. Ławniczak, L. Sirko, Phys. Rev. E 95, 052202 (2017), doi: 10.1103/PhysRevE.95.052202
• [49] A. Frisch, M. Mark, K. Aikawa, F. Ferlaino, J. Bohn, C. Makrides, A. Petrov, S. Kotochigova, Nature (London) 507, 475 (2014), doi: 10.1038/nature13137
• [50] J. Mur-Petit, R.A. Molina, Phys. Rev. E 92, 042906 (2015), doi: 10.1103/PhysRevE.92.042906
• [51] H.I. Liou, H.S. Camarda, F. Rahn, Phys. Rev. C 5, 1002 (1972), doi: 10.1103/PhysRevC.5.1002
• [52] T. Zimmermann, H. Köppel, L.S. Cederbaum, G. Persch, W. Demtröder, Phys. Rev. Lett. 61, 3 (1988), doi: 10.1103/PhysRevLett.61.3
• [53] U. Agvaanluvsan, G.E. Mitchell, J.F. Shriner Jr., M. Pato, Phys. Rev. C 67, 064608 (2003), doi: 10.1103/PhysRevC.67.064608
• [54] O. Bohigas, M. P. Pato, Phys. Lett. B 595, 171 (2004), doi: 10.1016/j.physletb.2004.05.065
• [55] R.A. Molina, J. Retamosa, L. Muñoz, A. Relaño, E. Faleiro, Phys. Lett. B 644, 25 (2007), doi: 10.1016/j.physletb.2006.10.058
• [56] A. Relaño, J.M.G. Gómez, R. A. Molina, J. Retamosa, E. Faleiro, Phys. Rev. Lett. 89, 244102 (2002), doi: 10.1103/PhysRevLett.89.244102
• [57] E. Faleiro, J. M. G. Gómez, R. A. Molina, L. Muñoz, A. Relaño, J. Retamosa, Phys. Rev. Lett. 93, 244101 (2004), doi: 10.1103/PhysRevLett.93.244101
• [58] J.M.G. Gómez, A. Relaño, J. Retamosa, E. Faleiro, L. Salasnich, M. Vraničar, M. Robnik, Phys. Rev. Lett. 94, 084101 (2005), doi: 10.1103/PhysRevLett.94.084101
• [59] E. Faleiro, U. Kuhl, R.A. Molina, L. Muñoz, A. Relaño, J. Retamosa, Phys. Lett. A 358, 251 (2006), doi: 10.1016/j.physleta.2006.05.029
• [60] R. Riser, V. Al. Osipov, E. Kanzieper, Phys. Rev. Lett. 118, 204101 (2017), doi: 10.1103/PhysRevLett.118.204101
• [61] D.S. Jones, Theory of Electromagnetism, Pergamon Press, Oxford 1964, p. 254
• [62] N. Savytskyy, A. Kohler, S. Bauch, R. Blümel, L. Sirko, Phys. Rev. E 64, 036211 (2001), doi: 10.1103/PhysRevE.64.036211

Identifiers

DOI

10.12693/APhysPolA.132.1672