Publication Date:
2011-06-15
Description:
A technically convenient signature of Anderson localization is exponential decay of the fractional moments of the Green function within appropriate energy ranges. We consider a random Hamiltonian on a lattice whose randomness is generated by the sign-indefinite single-site potential, which is however sign-definite at the boundary of its support. For this class of Anderson operators, we establish a finite-volume criterion which implies that the fractional moment decay property holds. This constructive criterion is satisfied at typical perturbative regimes, e.g. at spectral boundaries which satisfy “Lifshitz tail estimates” on the density of states and for sufficiently strong disorder. We also show how the fractional moment method facilitates the proof of exponential (spectral) localization for such random potentials. Content Type Journal Article Pages 1-29 DOI 10.1007/s00023-011-0112-5 Authors Alexander Elgart, 448 Department of Mathematics, McBryde Hall, Virginia Tech, Blacksburg, VA 24061, USA Martin Tautenhahn, Technische Universität Chemnitz, Fakultät für Mathematik, 09107 Chemnitz, Germany Ivan Veselić, Technische Universität Chemnitz, Fakultät für Mathematik, 09107 Chemnitz, Germany Journal Annales Henri Poincare Online ISSN 1424-0661 Print ISSN 1424-0637
Print ISSN:
1424-0637
Electronic ISSN:
1424-0661
Topics:
Mathematics
,
Physics
