1. Novosibirsk, May 23, 2008 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. Novosibirsk, May 23, 2008 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. Novosibirsk, May 23, 2008 Effective Hamiltonian approach to open systems intrinsic many-body states coupled to open channels with transition amplitude an effective non-Hermitian Hamiltonian withand Scattering matrix can be described by where

4. Novosibirsk, May 23, 2008 Isolated versus overlapped resonances The complex eigenvalues of are poles of - matrix with Control parameter of the coupling to continuum: whereis the mean level spacing Atwe have perfect coupling regime, For the segregation of widths occurs, with the formation of superradiant (wide) resonances andnarrow 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. Novosibirsk, May 23, 2008 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. Novosibirsk, May 23, 2008 Redistribution of widths Herefor

7. Novosibirsk, May 23, 2008 Average width Moldauer-Simonius for equivalent channels:

8. Novosibirsk, May 23, 2008 Resonance width distribution tail

9. Novosibirsk, May 23, 2008 Typical (elastic) cross sections

10. Novosibirsk, May 23, 2008 Average cross section Elastic enhancement factor

11. Novosibirsk, May 23, 2008 Dependence of elastic average cross section on the interaction strength

12. Novosibirsk, May 23, 2008 Enhancement factor vs interacton

13. Novosibirsk, May 23, 2008 Ericson Fluctuations some of the Ericson assumptions: some of the Ericson predictions: Lorentzian form (for cross sections) for

14. Novosibirsk, May 23, 2008 Cross section autocorrelation length vs average width Weisskopf relation: Contrary to Ericson prediction:

15. Novosibirsk, May 23, 2008 Conductance -- for “left” channels -- for “right” channels

16. Novosibirsk, May 23, 2008 Universal Conductance Fluctuations From Random Matrix Theory For uncorrelated cross sections : Correlations are important !

17. Novosibirsk, May 23, 2008 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. Novosibirsk, May 23, 2008 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. Novosibirsk, May 23, 2008 Analysis of correlations where forwe have the estimate : V.A. Garcia-Martin et al, Phys. Rev. Lett. 88 (2002) 143901 !!

20. Novosibirsk, May 23, 2008 1) For the first time the truly TBRE is considered in the framework of the Continuum Shell Model Conclusions 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. Novosibirsk, May 23, 2008 www.felix.izrailev.com

22. Novosibirsk, May 23, 2008 Divergence of the width variance

23. Novosibirsk, May 23, 2008 Resonance width variance vs interaction strength

24. Novosibirsk, May 23, 2008

25. Distribution of correlations -GOE

26. Novosibirsk, May 23, 2008 Dependence on the degree of internal chaos

27. Novosibirsk, May 23, 2008 Resonance width variance vs coupling to continuum

28. Novosibirsk, May 23, 2008 Dependence on the coupling to continuum

29. Novosibirsk, May 23, 2008 for the GOE: Mean conductance

30. Novosibirsk, May 23, 2008

32. Resonance residues-energies correlations

33. Novosibirsk, May 23, 2008 Distribution of correlations –TBRI model

34. Novosibirsk, May 23, 2008 Cross section distribution Comparison with Ericson exponential distribution

35. Novosibirsk, May 23, 2008 Fluctuations Black line: Analytical Results for GOE from E.D.Davis and D. Boose, Phys.Lett. B 211, 379 (1988).

36. Novosibirsk, May 23, 2008 Condactance Fluctuations vs M

37. Novosibirsk, May 23, 2008 Cross section fluctuations Ericson prediction:

38. Novosibirsk, May 23, 2008 Resonance width variance vs M Expectation (due to Ericson) -