Charge relaxation resistance in the Coulomb blockade problem

TL;DR

This paper investigates the energy dissipation in a small metallic island with Coulomb interactions, revealing universal behavior of charge relaxation resistance in different regimes of Coulomb blockade.

Contribution

It provides a unified analysis of dissipation in Coulomb blockade systems, deriving universal expressions for charge relaxation resistance across regimes.

Findings

Dissipation rate is universal in weak and strong Coulomb blockade regimes.

Quantum fluctuations significantly influence dissipation at not very low temperatures.

The derived formulas are expressed in terms of physically meaningful observables.

Abstract

We study the dissipation in a system consisting of a small metallic island coupled to a gate electrode and to a massive reservoir via single tunneling junction. The dissipation of energy is caused by a slowly oscillating gate voltage. We compute it in the regimes of weak and strong Coulomb blockade. We focus on the regime of not very low temperatures when electron coherence can be neglected but quantum fluctuations of charge are strong due to Coulomb interaction. The answers assume a particularly transparent form while expressed in terms of specially chosen physical observables. We discovered that the dissipation rate is given by a universal expression in both limiting cases.