Communications in Mathematical Physics

, Volume 153, Issue 3, pp 605–646 | Cite as

Limits of infinite interaction radius, dimensionality and the number of components for random operators with off-diagonal randomness

  • A. M. Khorunzhy
  • L. A. Pastur


We consider random one-body operators that are analogs of the statistical mechanics Hamiltonians with a varying interaction radiusR, the dimensionality of spaced and the number of the field components (orbitals)n. We prove that all the moments of the Green functions for nonreal energies of these operators converge asR, d, n→∞ to the products of the average Green functions, just as in the mean field approximation of statistical mechanics. We find in particular the selfconsistent equation for the limiting integrated density of states and the limiting form of the conductivity, which is nonzero on the whole support of the integrated density of states.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Green Function 
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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • A. M. Khorunzhy
    • 1
  • L. A. Pastur
    • 1
  1. 1.Institute for Low Temperature PhysicsAcademy of Sciences of UkraineKharkivUkraine

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