The electrical transport properties of one-dimensional tight-binding models, with correlation between diagonal and off-diagonal disorder, are obtained using Felderhof's method. A new local transformation eliminating the off-diagonal disorder is utilised. The characterisation of the type of correlation for the existence of a critical energy Ec, at which transmission exists, is found. It is a generalisation, in some sense, of the well known transmission at the band centre for the case with only off-diagonal disorder. For the high-wavenumber approximation we find explicitly the inverse localisation length which, close to Ec, behaves as mod E-Ec mod nu , with nu =1 at the edges of the band and nu =2 otherwise. The transmission for a wavepacket around Ec is analysed for samples of finite size.

We propose a quantum Hamiltonian for a transmission line with charge discreteness. The periodic line is composed of an inductance and a capacitance per cell. In every cell the charge operator satisfies a nonlinear equation of motion because of the discreteness of the charge. In the basis of one-energy per site, the spectrum can be calculated explicitly. We consider briefly the incorporation of electrical resistance in the line.

We consider a sequence of idealized measurements of time-separation $\Delta t$ onto a discrete one-dimensional disordered system. A connection with Markov chains is found. For a rapid sequence of measurements, a diffusive regime occurs and the diffusion coefficient $D$ is analytically calculated. In a general point of view, this result suggests the possibility to break the Anderson localization due to decoherence effects. Quantum Zeno effect emerges because the diffusion coefficient $D$ vanishes at the limit $\Delta t \to 0$.Comment: 8 pages, 0 figures, LATEX. accepted in Phys.Rev.

Current magnification is studied for a system of two rings with external magnetic flux; we have considered, in addition to self-inductance, a mutual inductance between the rings. The system is studied using a method recently proposed by Li and Chen, which takes into account the charge quantization of the system, allowing for a simplified description. We find that, for some values of the external flux enclosed by one of the rings, quantum current magnification exists in the other ring. This magnification effect is a purely quantum phenomenon, which is given here an alternative explanation, different from the detailed quantum-mechanical explanation.

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