C.1 FERMI-DIRAC Statistics

For FERMIons the occupation numbers are either 0 or $1$, and the sum in (C.12) is restricted to these values

$$\begin{array}{ll} Z_\mathrm{F}\ &\displaystyle = \ \prod_{i=1... ...left(1+e^{-\beta(E_{i}- E_\mathrm{F} )}\right)} \ . \end{array}$$ (C.13)

Taking the logarithm of both sides, one gets

$$\begin{array}{l}\displaystyle \Omega_\mathrm{F}(T,V, E_\mathr... ...left(1+e^{-\beta(E_{i}- E_\mathrm{F} )}\right)} \ , \end{array}$$ (C.14)

while the mean number of FERMIons is given by the FERMI-DIRAC distribution function

$$\begin{array}{l}\displaystyle n_\mathrm{F} \ \equiv \ \sum_{i... ...{e^{\beta \left(E_{i}- E_\mathrm{F} \right)}+1} \ . \end{array}$$ (C.15)

M. Pourfath: Numerical Study of Quantum Transport in Carbon Nanotube-Based Transistors