For distribution

[CM ICTP - Trieste]

SEMINAR on    Disorder and strong electron correlations



Thursday, 16 October      -  11:00 a.m.





Seminar Room,  Leonardo Bldg.- first floor



V. KRAVTSOV  ( I.C.T.P. )



"Subtle problems of one-dimensional localization: Devil's staircase  
of statistical anomalies "





Abstract



It is shown that in the old and celebrated problem of one-dimensional  
localization on a lattice with random on-site energies the joint  
probability distribution (JPD) of amplitudes and phases of random  
eigenfunction exhibits an anomaly at any rational filling factor. The  
principal anomaly at half-filling is described by the transfer-matrix  
equation with the two-dimensional (amplitude and phase) internal  
space and an explicit dependence on both co-ordinates. We show that  
the  zero mode variant of this equation is exactly solvable and find  
the unique solution for the JPD.