Localization of phonons in a two-component superlattice with random-thickness layers

A two-component superlattice film of $2N$ layers is considered and a dimensionally quantized spectrum of phonons is found. The problem of localization of phonons in the superlattice with random-thickness layers is investigated. The Landauer resistance of the transport of phonons and the correlation length is calculated exactly. For short range disorder the numerical analyses shows that, at frequency ω=0, there is a delocalized state and the correlation length index ν is equal to 2.