  Quantum transport through devices coupled to electron reservoirs can be
described in terms of the full counting statistics (FCS) of charge transfer.
Transport observables, such as conductance and shot-noise power are just
cumulants of FCS and can be obtained from the sample's average density of
transmission eigenvalues, which in turn can be obtained from a finite element
representation of the saddle-point equation of the Keldysh (or supersymmetric)
non-linear sigma-model, known as quantum circuit theory. Normal universal
metallic behavior in the semiclassical regime is controlled by the presence of
a Fabry-Perot singularity in the average density of transmission eigenvalues.
We present general conditions for the suppression of Fabry-Perot modes in the
semiclassical regime in a sample of arbitrary shape, a disordered conductor or
a network of ballistic quantum dots, which leads to an anomalous metallic
phase. Through a double-scaling limit, we derive a scaling equation for
anomalous metallic transport, in the form of a nonlinear differential equation,
which generalizes the ballistic-diffusive scaling equation of a normal metal.
The two-parameter stationary solution of our scaling equation generalizes
Dorokhov's universal single-parameter distribution of transmission eigenvalues.
We provide a simple interpretation of the stationary solution using a
thermodynamic analogy with a spin-glass system. As an application, we consider
a system formed by a diffusive wire coupled via a barrier to
normal-superconductor (NS) reservoirs. We observe anomalous reflectionless
tunneling, when all perfectly transmitting channels are suppressed, which
cannot be explained by the usual mechanism of disorder-induced opening of
tunneling channels.
