Localization versus chaos in disordered systems Hand waving derivation of significant results

by Alexander Burin

at Condensed Matter Theory Seminar

Wed, 09 Dec 2015, 13:30
Physics building (#54) room 207

Abstract

I am going to introduce the concept of Anderson localization for a single particle in an uncorrelated random potential Localized and delocalized behaviors will be illustrated qualitatively for the tight binding model in terms of resonant couplings for the particle hopping between three dimensional lattice sites with large number of neighbors and compared to the exact solution for the Bethe lattice by Abou Chacra Anderson and Thouless The delocalization for the long range hopping amplitude decreasing with the distance as R 3 or slower will be described The alternative definitions of localization in terms of Ioffe Regel criterion comparing mean free path with the particle wavelength and in terms of the level statistics Poisson in the localized state and Wigner Dyson in the localized state will be formulated and justified qualitatively The localization in low dimensions d 1 2 will be described using scaling theory of localization The similarity of the localization delocalization transition with the classical transition between integrable and chaotic behavior will be considered

Created on 06-12-2015 by Bar Lev, Yevgeny (ybarlev)
Updaded on 06-12-2015 by Bar Lev, Yevgeny (ybarlev)