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Photo made during the conference can be found on the web page (see album “Benasque”):. http://picasaweb.google.com/felix.izrailev. From closed to open 1D Anderson model:Transport versus spectral statistics. F.M.Izrailev Instituto de Física, BUAP, Puebla, México and

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  1. Photo made during the conference can be found on the web page (see album “Benasque”): http://picasaweb.google.com/felix.izrailev

  2. From closed to open 1D Anderson model:Transport versus spectral statistics F.M.Izrailev Instituto de Física, BUAP, Puebla, México and Michigan State University, USA In collaboration with: S. Sorathia (IFUAP, Puebla, Mexico) , G.Celardo (Univesita di Cattolica, Brescia, Italy), V. G. Zelevinsky (NSCL, E.Lansing, USA)

  3. Open 1D Anderson model Ideal semi-infinite LEFT lead Ideal semi-infinite RIGHT lead • How scattering properties depend on the degree of internal chaos and coupling strength ? Published in Phys. Rev. E (2012)

  4. Level statistics Spacing between neighbouring eigenvalues Spacing normalized to mean local spacing Ensemble average combined with average over eigenvalues that lie within a small energy window at the band centre Level spacing distribution - provides information about the degree of chaos Regular Chaotic Localized picket fence Wigner-Dyson Poisson Phenomenological spacing distribution interpolates between all three regimes 2D Coulomb gas on a circle repulsion parameter

  5. 2D Coulomb gas on a circle F.M.Izrailev, 1990-91 F.Dyson, 1962

  6. Delta function Chaotic Poisson Distribution of spacings between eigenvalues in the 1D Anderson model is the same as that for spacings between classical charged particles in the Coulomb gas model !

  7. Repulsion parameter is the properly normalized localization length !

  8. Non-Hermitian Effective Hamiltonian using the identity The exact non-Hermitian effective Hamiltonian Near the centre of the energy band this reduces to:

  9. Average transmission and variance - Coupling parameter for - Transmission coefficient - Variance of the transmission Excellent agreement between discrete Anderson model and formally exact analytical results for continuous system Analytical expressions for 1D continuous (i.e. not discrete) disordered media

  10. General case for any coupling: One can introduce an effective localization length: with where

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