Localization of states and kinetic properties of one-dimensional disordered systems
Annotatsiya
A number of results on the state, structure, and kinetics of one-dimensional disordered systems that have been obtained in recent years is presented. These results are deduced within the framework of a unified approach. The one-dimensional nature of the problem permits writing a closed system of dynamic equations, which are valid for each realization of the random potential v(x), for any characteristic quantity. If the potential is weak, or if E≪rc−2 (E is the energy, rc is the statistical correlation length of the potential), then it can be considered to be Gaussian white noise, when ⟨v(x) ⟩ = 0⟨v(x)v(x′) ⟩ = Dδ (x − x′). If, in addition, D/k3≪ 1 (condition for the quasiclassical approximation), then just as in the theory of parametric resonance, only the Fourier harmonics of the random potential corresponding to the momenta q,q±E where |q|≪E are significant in the dynamic equations indicated. This circumstance greatly simplifies the equations and permits completing the corresponding calculations. Application of this method to finding the attenuation of the wavefunction, the asymptotic properties of the transmission coefficient for a wave transmitted through a random barrier, the average Green’s function, the density-density correlation functions and the conductivity for high and low frequencies is described in the review.