Fermi–Dirac statistics

Equipment

• Fermi–Dirac distribution plot versus energy
• Virtual electron sea and Fermi surface in a 3D box
• Sliders for temperature, density/frequency, and state count

Procedure

1. Observe the Fermi step

   Set "Temperature" low and observe the distribution curve in figure 1: nearly every state below the Fermi surface is filled, and those above are empty — a consequence of the Pauli exclusion principle. Record the temperature readout and compare with $E_F/k_B$; the transition region is roughly $k_BT$ wide.

2. Raise temperature and density

   Slowly raise "Temperature" and watch the step smear around $\mu \approx E_F$: some electrons are excited above the Fermi surface leaving holes below. Then raise "Density / frequency" and watch $E_F$ grow, since $E_F \propto n^{2/3}$; compare with the electron-sea readout of figure 2.

3. Compare with classical statistics

   Set high temperature and low density so the Fermi–Dirac distribution approaches Maxwell–Boltzmann (when $\bar n_i \ll 1$, the denominator $e^{(\epsilon-\mu)/k_BT}+1 \approx e^{(\epsilon-\mu)/k_BT}$). Vary "Number of states" and note: each state holds at most one fermion — a sharp contrast with bosons.

Simulation

Experiment history

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