Friday's seminar

[Cond.Matt. & Stat.Mech.Section]

Seminar  on   Disorder and strong electron correlations



Friday, 9 April      -  11:00 a.m.



Luigi Stasi Seminar Room,  Leonardo Building - first floor



Oleg YEVTUSHENKO      ( Ludwig-Maximilians Universitaet, Muenchen )



"Critical scaling at the Anderson localization transition in the  
strong multifractality regime"



Abstract

We study dynamical scaling (DS) in disordered systems at (or close to)  
the point of the Anderson localization transition.  Wave functions of  
such systems are fractal.  DS is connected to strong spatial  
correlations of the wave functions.  These correlations are  
particularly nontrivial in the strong fractality regime where fractals  
are very sparse.  It has been conjectured [1] that there exists an  
exact relation between the exponent of DS and the 2nd fractal  
dimension.  To the best of our knowledge, neither existence of DS nor  
the relation between the exponents were checked analytically.

  We study DS and the critical exponents in the strong fractality  
regime using the model of almost diagonal random matrices with fractal  
eigenstates by analyzing asymptotic behavior of the return probability  
in the long time limit.  We have proven the DS to hold true up to the  
leading terms of 2nd loop of RG. Besides, we have found necessary  
conditions for the exact relation between the critical exponents.

  [1] J.T. Chalker and G.J. Daniell, Phys. Rev. Lett. 61, 593 (1988);  
J.T. Chalker, Physica A 167, 253 (1990).