Quantum-dot electrochemical potential (${\mu }_N=U(N)-U(N-1)$)

With $U(N)={\sum }_{i=1}^N{ϵ}_i+(Ne-Q_g{)}^2/(2C_{\Sigma })$, the addition electrochemical potential is ${\mu }_N={ϵ}_N+(N-1/2)e^2/C_{\Sigma }-e{Q}_g/C_{\Sigma }$. Gate and lead voltages enter $Q_g$. Adjacent addition potentials differ by an orbital spacing plus $e^2/C_{\Sigma }$.