Scaling of the localization length in linear electronic and vibrational systems with long-range correlated disorder

The localization lengths of long-range correlated disordered chains are studied for electronic wavefunctions in the Anderson model and for vibrational states. A scaling theory close to the band edge is developed in the Anderson model and supported by numerical simulations. This scaling theory is mapped onto the vibrational case at small frequencies. It is shown that for small frequencies, unexpectateley the localization length is smaller for correlated than for uncorrelated chains.