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Continuum shell model: From Ericson to conductance fluctuations

Continuum shell model: From Ericson to conductance fluctuations. Felix Izrailev Instituto de Física, BUAP, Puebla, México Michigan State University, E.Lansing, USA. in collaboration with :. G. Berman -- Los Alamos, USA L. Celardo -- Puebla, Mexico

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Continuum shell model: From Ericson to conductance fluctuations

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  1. Continuum shell model: From Ericson to conductance fluctuations Felix Izrailev Instituto de Física, BUAP, Puebla, México Michigan State University, E.Lansing, USA in collaboration with : G. Berman -- Los Alamos, USA L. Celardo -- Puebla, Mexico S. Sorathia -- Puebla, Mexico V. Zelevinsky – E.Lansing, USA

  2. Continuum shell model Resonance widths Cross sections Ericson fluctuations Conductance fluctuations Discussion Overview V.G.L.Celardo, F.M.Izrailev, V.G.Zelevinsky, G.P.Berman, Phys. Rev. E, 76 (2007) 031119, Phys. Lett. B 659 (2008) 170.

  3. Effective Hamiltonian approach to open systems coupled to intrinsic many-body states open channels with transition amplitude can be described by an effective non-Hermitian Hamiltonian with and Scattering matrix where

  4. Isolated versus overlapped resonances The complex eigenvalues of are poles of - matrix with Control parameter of the coupling to continuum: where is the mean level spacing At we have perfect coupling regime, For the segregation of widths occurs, with the formation of superradiant (wide) resonances and narrow ones V.P.Kleinwächer and I.Rotter, Phys.Rev.C 32 (1985) 1742; V.V.Sokolov and V.G.Zelevinsky, Phys. Lett. B 202 (1989) 10; Nucl. Phys. A 504 (1989) 562.

  5. Two-Body Interaction Model single-particle states two-body matrix elements number of single-particle states number of particles (“quasi-particles”) energy of single-particle states is considered in the many-particle basis of transition to chaos : V.V.Flambaum and F.M.I. – Phys. Rev. E 64 (2001) 036220

  6. Redistribution of widths Here for

  7. Average width Moldauer-Simonius for equivalent channels:

  8. Resonance width distribution tail

  9. Typical (elastic) cross sections

  10. Average cross section Elastic enhancement factor

  11. Dependence of elastic average cross section on the interaction strength

  12. Enhancement factor vs interacton

  13. Ericson Fluctuations for some of the Ericson assumptions: some of the Ericson predictions: Lorentzian form (for cross sections)

  14. Cross section autocorrelation length vs average width Weisskopf relation: Contrary to Ericson prediction:

  15. Conductance -- for “left” channels -- for “right” channels

  16. Universal Conductance Fluctuations From Random Matrix Theory For uncorrelated cross sections : Correlations are important !

  17. Correlations between different cross sections where Correlations are increasing with M , and they occur for both chaotic and regular intrinsic dynamics ! above, the total correction term for variance is shown, that is due to all correlations neglected in the Ericson theory

  18. Two types of correlations for cross sections where stand for correlations between cross sections having one joint channel, and -- for correlations between cross sections with no joint channels

  19. Analysis of correlations where for we have the estimate : V.A. Garcia-Martin et al, Phys. Rev. Lett. 88 (2002) 143901 !!

  20. Conclusions 1) For the first time the truly TBRE is considered in the framework of the Continuum Shell Model 2) The statistics of resonance widths are found to be very sensitive to the intrinsic chaos. 3) Contrary to Ericson expectations the fluctuations of resonance widths cannot be neglected even for large number of channels 4) The elastic enhancement factor strongly depends on the intrinsic interaction, thus the Hauser-Feshback formula must be modified 5) Universal conductance fluctuations are due to strong correlations between cross sections, they are different from Ericson fluctuations

  21. www.felix.izrailev.com

  22. Divergence of the width variance

  23. Resonance width variance vs interaction strength

  24. Distribution of correlations -GOE

  25. Dependence on the degree of internal chaos

  26. Resonance width variance vs coupling to continuum

  27. Dependence on the coupling to continuum

  28. Mean conductance for the GOE:

  29. Resonance residues-energies correlations

  30. Distribution of correlations –TBRI model

  31. Cross section distribution Comparison with Ericson exponential distribution

  32. Fluctuations Black line: Analytical Results for GOE from E.D.Davis and D. Boose, Phys.Lett. B 211, 379 (1988).

  33. Condactance Fluctuations vs M

  34. Cross section fluctuations Ericson prediction:

  35. Resonance width variance vs M Expectation (due to Ericson) -

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