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The author derives the Fokker-Planck equation for the distribution of the phase of the reflection amplitude for a disordered conductor of length L, using the invariant embedding method. The limiting (L= infinity ) stationary distribution in the strong-reflection regime is uniform provided that the localisation length is large compared with a Fermi wavelength. Next the author studies the joint distribution of the phase shift and of the time delay experienced by an incident electron in the conductor before being back-scattered. He obtains the explicit form of the marginal distribution for time delays for large L and strong reflections, using the uniformity of the phase distribution. The author applies it to study the spectral density of the surface charge fluctuation noise. An approximate analytical calculation yields an f-12/(3- alpha 2)/ spectrum where alpha >or=1.

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We reconsider the study of persistent currents in a disordered one-dimensional ring threaded by a magnetic flux ϕ, using he one-band tight-binding model for a ring of N-sites with random site energies. The secular equation for the eigenenergies expressed in terms of transfer matrices in the site representation is solved exactly to second order in a perturbation theory for weak disorder and fluxes differing from half-integer multiples of the flux quantum ϕ0=hc/e. From the equilibrium currents associated with the one-electron eigenstates we derive closed analytic expressions for the disorder averaged persistent current for even and odd numbers, Ne, of electrons in the ground state. Explicit discussion for the half-filled band case confirms that the persistent current is periodic with a period ϕ0, as in the absence of disorder, and that its amplitude is generally suppressed by the effect of the disorder. In comparison to previous results, based on an approximate analysis of the secular equation, the current suppression by disorder is strongly enhanced by a new periodic factor proportional to 1/ sin 2(2πϕ/ϕ0), for ϕ≠( integer )ϕ0/2.

We study analytically the eigenstates of a weakly disordered semi-infinite single-band tight-binding lattice in contact with an ordered parent lattice. We consider successively three simple types of correlated, continuously distributed site energies: a random dimer model, a random trimer model, and a random monomer-dimer model. In the dimer model the disordered chain lattice is partitioned into a collection of pairs of nearest-neighbor sites, where the two sites of a given pair are assigned a common independent random energy. The trimer model is similarly made up of triplets of nearest-neighbor sites having the same site energy taken as an independent random variable. Finally, the monomer-dimer model is defined as an alternate sequence of independent dimers and monomers with identically distributed site energies. The site energy randomness is described by Gaussian white noise and we restrict to energies of the pure system's energy band. We find that the averaged rates of exponential variation of site wave functions at finite distances X)&1 from the edge site of the disordered chain are anomalous at the band center (E =0), at the band edges, and at energies E =2cosam. , with a= -' for the dimer model and a= 6 3 3, and 6 for the trimer and monomer-dimer models. These results are relevant for transport behavior of finite disordered samples in the quasimetallic regime. On the other hand, we study the inverse localization lengths for the states whose energies are intermediate to the above special values. In the dimer model all the states in this energy range are localized, with an enhanced localization length. In the trimer and monomer-dimer models we obtain six delocalized states at fixed intermediate energies. The energies of the delocalized states separate domains where all states are localized from domains where all states are antilocalized. The antilocalized states discussed in this paper have the usual Bloch form up to the edge site of the ordered lattice, beyond which they decrease exponentially into the disordered lattice. We also study the effect of disorder on the phase of site wave functions.