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Anderson model; absolutely continuous spectrum; mobility edge; decaying randomness

In this paper we consider some Anderson type models, with free parts having long range tails and with the random perturbations decaying at different rates in different directions and prove that there is a.c. spectrum in the model which is pure. In addition, we show that there is pure point spectrum outside some interval. Our models include potentials decaying in all directions in which case absence of singular continuous spectrum is also shown.

M Krishna^{1 2} K B Sinha^{1 2 3}

1. Institute of Mathematical Sciences, Taramani, Chennai - 600 113, India
2. Indian Statistical Institute, 7 SJS Sansanwal Marg, New Delhi - 110 016, India
3. Indian Statistical Institute, 203, BT Road, Kolkata - 700 035, India

Published

May 2001

Manuscript received

11 May 2000

Manuscript revised

17 November 2000