Scientific Calendar Event



Starts 9 Apr 2010 12:00
Ends 9 Apr 2010 20:00
Central European Time
ICTP
Leonardo da Vinci Building Luigi Stasi Seminar Room
Strada Costiera, 11 I - 34151 Trieste (Italy)
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).
  • M. Poropat