2002/03/11 by Christian Ferrari, Ferrari, Christian, Nicolas Macris +1 · 1 citation
Mathematics · Physics and Astronomy · #Quantum and electron transport phenomena #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/0203016
To appear in J. Oper. Theor
arxiv created 2002/03/11 · arxiv updated 2009/11/30
In this note we review spectral properties of magnetic random Schroedinger operators Homega=H0+Vomega + Ul + Ur defined on L2(R x [-L/2,L/2],dx dy) with periodic boundary conditions along y. Ul and Ur are two confining potentials for x<-L/2 and x>L/2 respectively and vanish for -L/2<x<L/2. We describe the spectrum in two energy intervals and we classify it according to the quantum mechanical current of eigenstates along the periodic direction. The first interval lies in the first Landau band of the bulk Hamiltonian, and contains intermixed eigenvalues with a quantum mechanical current of O(1) and O(e-gamma B(log L)2) respectively. The second interval lies in the first spectral gap of the bulk Hamiltonian, and contains only eigenvalues with a quantum mechanical current of O(1).