Probing Eigenfunction Nonorthogonality by Parametric Shifts of Resonance Widths

• Authors: D. Savin , J. De Vaulx
• Languages of publication: EN

Abstracts

EN

Recently, it has been shown that the change of resonance widths in an open system under a perturbation of its interior is a sensitive indicator of the nonorthogonality of resonance states. We apply this measure to quantify parametric motion of the resonances. In particular, a strong redistribution of the widths is linked with the maximal degree of nonorthogonality. Then for weakly open chaotic systems we discuss the effect of spectral rigidity on the statistical properties of the parametric width shifts, and derive the distribution of the latter in a picket-fence model with equidistant spectrum.

Keywords

EN

03.65.Nk; 05.45.Mt; 05.60.Gg

Discipline

• 03.65.Nk: Scattering theory
• 05.60.Gg: Quantum transport
• 05.45.Mt: Quantum chaos; semiclassical methods

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2013
• Volume: 124
• Issue: 6
• Pages: 1074-1077

Dates

published

2013-12

Contributors

author

D. Savin

• Department of Mathematical Sciences, Brunel University, Uxbridge, UB8 3PH, United Kingdom

author

J. De Vaulx

• Department of Mathematical Sciences, Brunel University, Uxbridge, UB8 3PH, United Kingdom

References

• [1] C. Mahaux, H.A. Weidenmüller, Shell-Model Approach to Nuclear Reactions, North-Holland, Amsterdam, 1969
• [2] J.J.M. Verbaarschot, H.A. Weidenmüller, M.R. Zirnbauer, Phys. Rep. 129, 367 (1985)
• [3] V.V. Sokolov, V.G. Zelevinsky, Nucl. Phys. A 504, 562 (1989)
• [4] Y.V. Fyodorov, H.-J. Sommers, J. Math. Phys. 38, 1918 (1997)
• [5] I. Rotter, J. Phys. A, Math. Theor. 42, 153001 (2009)
• [6] Y.V. Fyodorov, D.V. Savin, in: Oxford Handbook of Random Matrix Theory, Eds. G. Akemann, J. Baik, P. Di Francesco, OUP, Oxford, 2011, p. 703
• [7] J.S. Bell, J. Steinberger, in: Proc. Oxford Int. Conf. on Elementary Particles, 1965, Eds. R.G. Moorhouse, A.E. Taylor, T.R. Walsh, Rutherford Laboratory, England 1966, p. 195
• [8] V.V. Sokolov, P. von Brentano, Nucl. Phys. A 578, 134 (1994)
• [8a] V.V. Sokolov, I. Rotter, D.V. Savin, M. Müller, Phys. Rev. C 56, 1031 (1997)
• [8b] V.V. Sokolov, I. Rotter, D.V. Savin, M. Müller, ibid. 56, 1044 (1997)
• [9] D.V. Savin, V.V. Sokolov, Phys. Rev. E 56, R4911 (1997)
• [10] J.T. Chalker, B. Mehlig, Phys. Rev. Lett. 81, 3367 (1998)
• [11] K. Peterman, IEEE J. Quant. Electron. 15, 566 (1979)
• [12] H. Schomerus, K.M. Frahm, M. Patra, C.W.J. Beenakker, Physica A 278, 469 (2000)
• [13] Y.-H. Kim, U. Kuhl, H.-J. Stöckmann, P.W. Brouwer, Phys. Rev. Lett. 94, 036804 (2005)
• [14] E.N. Bulgakov, I. Rotter, A.F. Sadreev, Phys. Rev. E 74, 056204 (2006)
• [15] D.V. Savin, O. Legrand, F. Mortessagne, Europhys. Lett. 76, 774 (2006)
• [16] C. Poli, D.V. Savin, O. Legrand, F. Mortessagne, Phys. Rev. E 80, 046203 (2009)
• [17] J. Wiersig, S.W. Kim, M. Hentschel, Phys. Rev. A 78, 053809 (2008)
• [17a] J. Wiersig, ibid. 84, 063828 (2011)
• [18] O.I. Lobkis, R.L. Weaver, J. Acoust. Soc. Am. 108, 1480 (2000)
• [19] O. Xeridat, C. Poli, O. Legrand, F. Mortessagne, P. Sebbah, Phys. Rev. E 80, 035201(R) (2009)
• [20] L.N. Trefethen, SIAM Rev. 39, 383 (1997)
• [21] Y.V. Fyodorov, D.V. Savin, Phys. Rev. Lett. 108, 184101 (2012)
• [22] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, 1966
• [23] A.I. Magunov, I. Rotter, S.I. Strakhova, J. Phys. B, At. Mol. Opt. Phys. 32, 1669 (1999)
• [24] M. Glück, A.R. Kolovsky, H.J. Korsch, Phys. Rep. 366, 103 (2002)
• [25] A. Volya, V. Zelevinsky, Phys. Rev. C 67, 054322 (2003)
• [26] E. Hernández, A. Jáuregui, A. Mondragón, Phys. Rev. E 84, 046209 (2011)
• [27] S. Bittner, B. Dietz, U. Günther, H.L. Harney, M. Miski-Oglu, A. Richter, F. Schäfer, Phys. Rev. Lett. 108, 024101 (2012)
• [28] D.C. Brody, E.-M. Graefe, Entropy 15, 3361 (2013)
• [29] U. Kuhl, R. Höhmann, J. Main, H.-J. Stöckmann, Phys. Rev. Lett. 100, 254101 (2008)
• [30] W.D. Heiss, J. Phys. A 45, 444016 (2012)
• [31] H. Eleuch, I. Rotter, Phys. Rev. E 87, 052136 (2013)

Identifiers

DOI

10.12693/APhysPolA.124.1074