Special energies and special frequencies (Q1822414)

''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 Schrödinger operator describing an alloy or its discrete analogue. Using the phase method we exactly determine a bilateral Lifšic 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 \(C^{\infty}\).