Zoran Skoda
Fano-Anderson model

This model was discovered simultaneously in atomic physics by Fano and in condensed matter physics by Anderson.

It involves a continuous spectrum of free particles with energies ϵ k\epsilon_k and number operator n k=a k a kn_k = a_k^\dagger a_k and a single extra particle in state |v|v\rangle and energy ϵ v\epsilon_v. The Hamiltonian in this model is of the form

H= kϵ kn k+ϵ vn v+ k(V ka k a v+V¯ ka v a k) H = \sum_k \epsilon_k n_k + \epsilon_v n_v + \sum_k (V_k a_k^\dagger a_v + \bar{V}_k a_v^\dagger a_k)

The complex coefficients V kV_k and V¯ k\bar{V}_k are called the hopping matrix elements as they encode the hopping transitions between the single particle state and continuum.

  • Ugo Fano, Effects of configuration interaction on intensities and phase shifts, Phys. Rev. 124, 1866 (1961) doi
  • P.W. Anderson, Phys. Rev.164, 41 (1961)
  • G.D. Mahan, Many-particle physics (New York, Plenum Press, 1990) 272–285
  • Michele Cini, Topics and methods in condensed matter theory, 2007

It is related also to the classical theory of

  • J. von Neumann, E. Wigner, Phys. Z. 30, 465 (1929)

Last revised on October 15, 2016 at 08:15:15. See the history of this page for a list of all contributions to it.