Narrow Results

The conserving sum rules for the electron gas form a set of fundamental and powerful constraints on the description of electronic transport, at any length scale. We examine the particular role of the compressibility sum rule for open mesoscopic conductors, and show that the compressibility in such systems is absolutely invariant under nonequilibrium transport. The compressibility sum rule provides a stringent consistency check on models of mesoscopic conduction.

The standard physical model of contemporary mesoscopic noise and transport consists in a phenomenologically based approach, proposed originally by Landauer and since continued and amplified by Büttiker, Imry and others. Throughout all the years of its gestation and growth, it is surprising that the Landauer–Büttiker approach to mesoscopics has matured with scant attention to the conserving properties lying at its roots: that is, at the level of actual microscopic principles. We systematically apply the sum rules for the electron gas to clarify the issue of conservation within the standard model of mesoscopic conduction. Noise, as observed in quantum point contacts, provides the vital clue.

We discuss recent developments in building models for GPDs that are based on the formalism of double distributions (DDs). A special attention is given to a careful analysis of the singularity structure of DDs. The DD formalism is applied to construction of a model GPDs with a singular Regge behavior. Within the developed DD-based approach, we discuss the structure of GPD sum rules. It is shown that separation of DDs into the so-called "plus" part and the D-term part may be treated as a renormalization procedure for the GPD sum rules. This approach is compared with an alternative prescription based on analytic regularization.