Zeitschrift für Physik B Condensed Matter

, Volume 35, Issue 3, pp 207–210 | Cite as

The mobility edge problem: Continuous symmetry and a conjecture

  • Franz Wegner


An apparently overlooked symmetry of the disordered electron problem is derived. It yields the well-known Ward-identity connecting the one- and two-particle Green's function. This symmetry and the apparent shortrange behaviour of the averaged one-particle Green's function are used to conjecture that the critical behaviour near the mobility edge coincides with that of interacting matrices which have two different eigenvalues of multiplicity zero (due to replicas). As a consequence the exponents of the d.c. conductivity is expected to approach 1 for real matrices and 1/2 for complex matrices as the dimensionality of the system approaches two from above. In two dimensions no metallic conductivity is expected.


Spectroscopy Neural Network State Physics Complex System Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Franz Wegner
    • 1
  1. 1.Institut für Theoretische PhysikUniversität HeidelbergHeidelberg 1Federal Republic of Germany

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