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2017 | 132 | 6 | 1688-1694
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Fluctuations and Correlations in Scattering on a Resonance Coupled to a Chaotic Background

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EN
We discuss and briefly overview recent progress with studying fluctuations in scattering on a resonance state coupled to the background of many chaotic states. Such a problem arises naturally, e.g., when dealing with wave propagation in the presence of a complex environment. Using a statistical model based on random matrix theory, we obtain a number of nonperturbative results for various statistics of scattering characteristics. This includes the joint and marginal distributions of the reflection and transmission intensities and phases, which are derived exactly at arbitrary coupling to the background with finite absorption. The intensities and phases are found to exhibit highly non-trivial statistical correlations, which remain essential even in the limit of strong absorption. In the latter case, we also consider the relevant approximations and their accuracy. As an application, we briefly discuss the statistics of the phase rigidity (or mode complexness) in such a scattering situation.
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  • Department of Mathematics, Brunel University London, Uxbridge, UB8 3PH, United Kingdom
References
  • [1] C. Mahaux, H.A. Weidenmüller, Shell-model Approach to Nuclear Reactions (North-Holland, Amsterdam, 1969)
  • [2] H.M. Nussenzveig, Causality and Dispersion Relations (Academic Press, New York, 1972), doi: 10.1016/S0076-5392(08)63157-4ph
  • [3] P.A. Mello, N. Kumar, Quantum Transport in Mesoscopic Systems: Complexity and Statistical Fluctuations (Oxford University Press, Oxford, 2004), doi: 10.1093/acprof:oso/9780198525820.001.0001ph
  • [4] D.V. Savin, Resonances in wave scattering, in Advanced Techniques in Applied Mathematics (World Scientific, 2016) Chap.2, p. 35, doi: 10.1142/9781786340238_0002
  • [5] H. Nishioka, H.A. Weidenmüller, Phys. Lett. B 157, 101 (1985), doi: 10.1016/0370-2693(85)91525-4
  • [6] V.V. Sokolov, V. Zelevinsky, Phys. Rev. C 56, 311 (1997), doi: 10.1103/PhysRevC.56.311
  • [7] A. Bohr, B.R. Mottelson, Nuclear Structure (Benjamin, New York, 1969)
  • [8] H.L. Harney, A. Richter, H.A. Weidenmüller, Rev. Mod. Phys. 58, 607 (1986), doi: 10.1103/RevModPhys.58.607
  • [9] V.V. Sokolov, I. Rotter, D.V. Savin, M. Müller, Phys. Rev. C 56, 1031 (1997), doi: 10.1103/PhysRevC.56.1031
  • [9a] V.V. Sokolov, I. Rotter, D.V. Savin, M. Müller, Phys. Rev. C 56, 1044 (1997), doi: 10.1103/PhysRevC.56.1044
  • [10] J.-Z. Gu, H. Weidenmüller, Nucl. Phys. A 660, 197 (1999), doi: 10.1016/S0375-9474(99)00362-0
  • [11] V. Zelevinsky, A. Volya, Phys. Scr. 91, 033006 (2016), doi: 10.1088/0031-8949/91/3/033006
  • [12] S. Aberg, T. Guhr, M. Miski-Oglu, A. Richter, Phys. Rev. Lett. 100, 204101 (2008), doi: 10.1103/PhysRevLett.100.204101
  • [13] T. Guhr, Acta Phys. Pol. A 116, 741 (2009), doi: 10.12693/APhysPolA.116.741
  • [14] V.V. Sokolov, J. Phys. A 43, 265102 (2010), doi: 10.1088/1751-8113/43/26/265102
  • [15] A. Morales, A.D. de Anda, J. Flores, L. Gutiérrez, R.A. Méndez-Sánchez, G. Monsivais, P. Mora, Europhys. Lett. 99, 54002 (2012), doi: 10.1209/0295-5075/99/54002
  • [16] D.V. Savin, M. Richter, U. Kuhl, O. Legrand, F. Mortessagne, Phys. Rev. E 96, 032221 (2017), doi: 10.1103/PhysRevE.96.032221
  • [17] D.V. Savin, arXiv: 1709.10479 (2017) http://arXiv.org/abs/1709.10479
  • [18] D.V. Savin, arXiv: 1710.11071 (2017) http://arXiv.org/abs/1710.11071
  • [19] T. Guhr, A. Müller-Groeling, H.A. Weidenmüller, Phys. Rep. 299, 189 (1998), doi: 10.1016/S0370-1573(97)00088-4
  • [20] H.-J. Stöckmann, Quantum Chaos: An Introduction (Cambridge University Press, Cambridge, UK, 1999)
  • [21] Y.V. Fyodorov, D.V. Savin, in The Oxford Handbook of Random Matrix Theory, edited by G. Akemann, J. Baik, P. Di Francesco (Oxford University Press, UK, 2011) Chap.34, p. 703, [arXiv: 1003.0702] http://arXiv.org/abs/
  • [22] Y.V. Fyodorov, D.V. Savin, JETP Lett. 80, 725 (2004), doi: 10.1134/1.1868794
  • [23] D.V. Savin, H.-J. Sommers, Y.V. Fyodorov, JETP Lett. 82, 544 (2005), doi: 10.1134/1.2150877
  • [24] Y.V. Fyodorov, D.V. Savin, H.-J. Sommers, J. Phys. A 38, 10731 (2005), doi: 10.1088/0305-4470/38/49/017
  • [25] D.V. Savin, H.-J. Sommers, Phys. Rev. E 68, 036211 (2003), doi: 10.1103/PhysRevE.68.036211
  • [26] P.A. Mello, in Mesoscopic Quantum Physics, Proceedings of the Les-Houches Summer School, Session LXI, edited by E. Akkermans, G. Montambaux, J.-L. Pichard, J. Zinn-Justin (Elsevier, 1995) p. 435
  • [27] U. Kuhl, M. Martínez-Mares, R.A. Méndez-Sánchez, H.-J. Stöckmann, Phys. Rev. Lett. 94, 144101 (2005), doi: 10.1103/PhysRevLett.94.144101
  • [28] R. Schäfer, T. Gorin, T.H. Seligman, H.-J. Stöckmann, J. Phys. A 36, 3289 (2003), doi: 10.1088/0305-4470/36/12/325
  • [29] U. Kuhl, H.-J. Stöckmann, R. Weaver, J. Phys. A 38, 10433 (2005), doi: 10.1088/0305-4470/38/49/001
  • [30] S.O. Rice, Bell Syst. Tech. J. 27, 109 (1948), doi: 10.1002/j.1538-7305.1948.tb01334.x
  • [31] M.D. Yacoub, G. Fraidenraich, J.C. S.S. Filho, Electron. Lett. 41, 259 (2005), doi: 10.1049/el:20057014
  • [32] S. van Langen, P.W. Brouwer, C.W.J. Beenakker, Phys. Rev. E 55, R1 (1997), doi: 10.1103/PhysRevE.55.R1
  • [33] I. Rotter, J. Phys. A 42, 153001 (2009), doi: 10.1088/1751-8113/42/15/153001
  • [34] P.W. Brouwer, Phys. Rev. E 68, 046205 (2003), doi: 10.1103/PhysRevE.68.046205
  • [35] Y.-H. Kim, U. Kuhl, H.-J. Stöckmann, P.W. Brouwer, Phys. Rev. Lett. 94, 036804 (2005), doi: 10.1103/PhysRevLett.94.036804
  • [36] R. Pnini, B. Shapiro, Phys. Rev. E 54, R1032 (1996), doi: 10.1103/PhysRevE.54.R1032
  • [37] O.I. Lobkis, R.L. Weaver, J. Acoust. Soc. Am. 108, 1480 (2000), doi: 10.1121/1.1289920
  • [38] J. Barthëlemy, O. Legrand, F. Mortessagne, Europhys. Lett. 70, 162 (2005), doi: 10.1209/epl/i2005-10005-7
  • [39] D.V. Savin, O. Legrand, F. Mortessagne, Europhys. Lett. 76, 774 (2006), doi: 10.1209/epl/i2006-10358-3
  • [40] C. Poli, D.V. Savin, O. Legrand, F. Mortessagne, Phys. Rev. E 80, 046203 (2009), doi: 10.1103/PhysRevE.80.046203
  • [41] E. Kanzieper, V. Freilikher, Phys. Rev. B 54, 8737 (1996), doi: 10.1103/PhysRevB.54.8737
  • [42] S. Hemmady, X. Zheng, J. Hart, T.M. Antonsen, E. Ott, S.M. Anlage, Phys. Rev. E 74, 036213 (2006), doi: 10.1103/PhysRevE.74.036213
  • [43] B. Köber, U. Kuhl, H.-J. Stöckmann, T. Gorin, D.V. Savin, T.H. Seligman, Phys. Rev. E 82, 036207 (2010), doi: 10.1103/PhysRevE.82.036207
  • [44] 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
  • [45] J.-H. Yeh, T.M. Antonsen, E. Ott, S.M. Anlage, Phys. Rev. E 85, 015202 (2012), doi: 10.1103/PhysRevE.85.015202
  • [46] U. Kuhl, O. Legrand, F. Mortessagne, Fortschr. Phys. 61, 404 (2013), doi: 10.1002/prop.201200101
  • [47] G. Gradoni, J.-H. Yeh, B. Xiao, T.M. Antonsen, S.M. Anlage, E. Ott, Wave Motion 51, 606 (2014), doi: 10.1016/j.wavemoti.2014.02.003
  • [48] S. Kumar, A. Nock, H.-J. Sommers, T. Guhr, B. Dietz, M. Miski-Oglu, A. Richter, F. Schäfer, Phys. Rev. Lett. 111, 030403 (2013), doi: 10.1103/PhysRevLett.111.030403
  • [49] A. Nock, S. Kumar, H.-J. Sommers, T. Guhr, Ann. Phys. 342, 103 (2014), doi: 10.1016/j.aop.2013.11.006
  • [50] S. Kumar, B. Dietz, T. Guhr, A. Richter, arXiv: 1711.08320 (2017). http://arXiv.org/abs/1711.08320
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bwmeta1.element.bwnjournal-article-appv132n6p07kz
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