Cluster transfer matrix method for the single electron box

TL;DR

This paper introduces a cluster transfer matrix method to analyze the single electron box, effectively calculating electron number and its derivatives at finite temperatures, comparable to Monte Carlo and renormalization group techniques.

Contribution

The paper presents a novel cluster transfer matrix approach that matches the effectiveness of established methods for studying single electron boxes.

Findings

Accurately computes average electron number versus polarization charge.

Demonstrates the method's effectiveness at finite temperatures.

Shows comparable results to Monte Carlo and renormalization group methods.

Abstract

With the newly developed cluster transfer matrix method, we calculate the average electron number n vs nx (the polarization charge) for varying junction conductance and its first derivative at nx=0 for finite temperatures, and demonstrate that the new method is as powerful as the Monte Carlo and renormalization group methods.