THEORY OF MESOSCOPIC TRANSPORT IN DISORDERED WIRES

We present a nonperturbative microscopic approach to mesoscopic transport in disordered phase-coherent systems, based on the exact scaling (''evolution'') equations for the transfer and scattering matrices and Landauer's formula. In this work, we apply the method to the quasi-one-dimensional limit and provide a systematic treatment of all the transport regimes present. In the ballistic regime, we consider the transition between the Sharvin and Drude conductances and recover many exact results of the classic transport theory. In the weak localization (diffusive) regime, the bulk of the probability distribution of the conductance of a wire is shown to be normal Gaussian, in agreement with the predictions based on the nonlinear sigma model. The formalism developed provides a convenient way of calculating the quantum-interference effects not only in the conductance but in arbitrary linear statistics on the transmission eigenvalues as well. In the classic diffusive limit, the eigenvalue density is independent on the geometry of the conductor. In the strong localization regime, the distribution of the conductance is found to coincide with Abrikosov's solution (approximately log normal), describing a purely one-dimensional chain. The calculated value of the localization length is proportional to the cross section of the wire, in precise agreement with Efetov's result obtained with the use of supersymmetric techniques. We recover the theory of the coherent backscattering peak and calculate the enhancement factor. The angular structure of the transmission and reflection coefficients is calculated exactly and found to be nonisotropic, which is contrary to the standard isotropy assumption of the existing macroscopic models. The approach is shown to provide microscopical proof of the Dorokhnov-Mello-Pereyra-Kumar equation for the distribution of transmission eigenvalues within the realistic model of a wire with the isotropic dispersion law.