fermi-dirac-distro.typ

#import "@preview/cetz:0.3.3": canvas, draw
#import "@preview/cetz-plot:0.1.1": plot
#import draw: content, line, bezier

#set page(width: auto, height: auto, margin: 8pt)

// Fermi-Dirac distribution function
#let n_F(x, beta, mu: 1) = {
  1 / (calc.exp(beta * (x - mu)) + 1)
}

#canvas({
  draw.set-style(
    axes: (
      y: (label: (anchor: "south-west")),
      x: (label: (anchor: "north-east")),
    ),
  )

  plot.plot(
    size: (8, 7),
    x-label: [$epsilon$ / $mu$],
    y-label: $n(epsilon)$,
    x-min: 0,
    x-max: 2.3,
    y-min: 0,
    y-max: 1.2,
    x-tick-step: .5,
    y-tick-step: .5,
    y-ticks: (0.5, 1),
    axis-style: "left",
    legend: (5.5, 2.5),
    legend-style: (item: (spacing: 0.2), padding: 0.15),
    {
      // Plot distributions for different temperatures
      let chem-pot = 1

      // T = μ/5k_B (red curve)
      plot.add(
        style: (stroke: red + 1.5pt),
        domain: (0, 2.3),
        samples: 150,
        x => n_F(x, 5),
        label: $k_"B" T = 1 / 5 mu$,
      )

      // T = μ/25k_B (orange curve)
      plot.add(
        style: (stroke: orange + 1.5pt),
        domain: (0, 2.3),
        samples: 150,
        x => n_F(x, 25),
        label: $k_"B" T = 1 / 25 mu$,
      )

      // T = 0 (blue step function)
      let points = ((0, 1), (chem-pot, 1), (chem-pot, 0), (2.3, 0))
      plot.add(
        style: (stroke: blue + 1.5pt),
        points,
        label: $T = 0$,
      )

      plot.add-vline(0.8, style: (stroke: (dash: "dashed", thickness: 0.5pt)))
      plot.add-vline(1.2, style: (stroke: (dash: "dashed", thickness: 0.5pt)))

      // Add thermal fluctuation indicators
      plot.add-hline(
        1.1,
        min: 0.8,
        max: 1.2,
        style: (
          stroke: (thickness: 0.5pt),
          mark: (symbol: "stealth", stroke: 0.5pt, fill: black, scale: .1),
        ),
      )
    },
  )

  content(
    (3.5, 6.5),
    $prop 1 / beta$,
    anchor: "south",
  )
})