Special energies and special frequencies

Abstract

Special frequencies" have been asserted to be zeros of the density of frequencies corresponding to a random chain of coupled oscillators. Our investigation includes both this model and the random one-dimensional Schrόdinger operator describing an alloy or its discrete analogue. Using the phase method we exactly determine a bilateral Lifsic asymptotic of the integrated density of states k(E) at special energies E s , which is not only of the classical type exp(c/\E -E s \ 1/2 ) but also exp(c'/\E -E s \) is a typical behaviour. In addition, other asymptotics occur, e.g. \E -E s \ c '\ which show that k(E) need not be C 00 .