Nonequilibrium theory of Coulomb blockade in open quantum dots

TL;DR

This paper develops a non-equilibrium theoretical framework for weak Coulomb blockade effects in open quantum dots, unifying different approaches and analyzing conductance corrections and pumped current.

Contribution

It introduces a 1/N expansion method to address deficiencies in previous models, providing a unified approach to Coulomb blockade in open quantum dots.

Findings

Interactions do not affect averaged conductance in ideal contacts.

The theory unifies phase functional and bosonization approaches.

Application to quantum pump shows detailed non-equilibrium effects.

Abstract

We develop a non-equilibrium theory to describe weak Coulomb blockade effects in open quantum dots. Working within the bosonized description of electrons in the point contacts, we expose deficiencies in earlier applications of this method, and address them using a 1/N expansion in the inverse number of channels. At leading order this yields the self-consistent potential for the charging interaction. Coulomb blockade effects arise as quantum corrections to transport at the next order. Our approach unifies the phase functional and bosonization approaches to the problem, as well as providing a simple picture for the conductance corrections in terms of renormalization of the dot's elastic scattering matrix, which is obtained also by elementary perturbation theory. For the case of ideal contacts, a symmetry argument immediately allows us to conclude that interactions give no signature in the averaged conductance. Non-equilibrium applications to the pumped current in a quantum pump are worked out in detail.