add single-head-attention.typ converted from single-head-attention.tex

add critical-temperature.typ converted from critical-temperature.tex
add gas-pressure-on-wall.typ converted from gas-pressure-on-wall.tex (prev wall.tex)

rename propagators to qft-propagators

assets/critical-temperature/critical-temperature.typ

@@ -0,0 +1,70 @@
+#import "@preview/cetz:0.3.2": canvas, draw
+#import "@preview/cetz-plot:0.1.1": plot
+
+#set page(width: auto, height: auto, margin: 8pt)
+
+#let tc = 1
+
+// Define the three functions
+#let f1(x) = {
+  if x == tc { return 0 }
+  calc.sqrt(3) * calc.pow(tc / x - 1, 1 / 2)
+}
+
+#let f2(x) = calc.sqrt(3) * calc.pow(x / tc, 3 / 2)
+
+#let f3(x) = {
+  if x == tc { return 0 }
+  calc.sqrt(3) * calc.pow(x / tc, 3 / 2) * calc.pow(tc / x - 1, 1 / 2)
+}
+
+#canvas({
+  draw.set-style(
+    axes: (
+      y: (label: (anchor: "north-west", offset: -0.2), mark: (end: "stealth", fill: black)),
+      x: (label: (anchor: "north", offset: 0.2), mark: (end: "stealth", fill: black)),
+    ),
+  )
+
+  plot.plot(
+    size: (10, 8),
+    x-label: $T$,
+    x-min: 0,
+    x-max: 1.1,
+    y-min: 0,
+    y-max: 2.8,
+    axis-style: "left",
+    x-tick-step: 0.2,
+    y-tick-step: 0.5,
+    legend: (6.5, 8.5),
+    legend-style: (item: (spacing: 0.15), padding: 0.25, stroke: .5pt),
+    {
+      // First function (blue)
+      plot.add(
+        style: (stroke: blue + 1.5pt),
+        samples: 100,
+        domain: (0.01, 1),
+        f1,
+        label: $sqrt(3)(T_c \/ T - 1)^(1 / 2)$,
+      )
+
+      // Second function (red)
+      plot.add(
+        style: (stroke: red + 1.5pt),
+        samples: 50,
+        domain: (0, 1.1),
+        f2,
+        label: $sqrt(3)(T \/ T_c)^(3 / 2)$,
+      )
+
+      // Third function (orange)
+      plot.add(
+        style: (stroke: orange + 1.5pt),
+        samples: 125,
+        domain: (0.01, 1),
+        f3,
+        label: $m_c(T)$,
+      )
+    },
+  )
+})

assets/gas-pressure-on-wall/gas-pressure-on-wall.typ

@@ -0,0 +1,77 @@
+#import "@preview/cetz:0.3.2": canvas, draw
+#import "@preview/modpattern:0.1.0": modpattern
+
+#set page(width: auto, height: auto, margin: 8pt)
+
+#let hatched = modpattern(
+  (.2cm, .2cm),
+  std.line(start: (0%, 100%), end: (100%, 0%), stroke: 0.5pt),
+)
+
+#let lennard-jones(x, A, B, alpha) = {
+  -A * calc.exp(-alpha * x) + B * calc.exp(-2 * alpha * x)
+}
+
+#canvas({
+  import draw: line, content, rect, on-layer
+
+  let arrow-style = (mark: (end: ">", fill: black, scale: 0.7))
+  let wall-width = 0.5
+
+  // Draw axes
+  line((-0.1, 0), (6.2, 0), ..arrow-style, name: "x-axis")
+  line((0, -0.7), (0, 4), ..arrow-style, name: "y-axis")
+
+  // Add axis labels
+  content((rel: (-0.2, 0.3), to: "x-axis.end"), $x$, name: "x-label")
+  content((rel: (0.5, 0), to: "y-axis.end"), $U(x)$, name: "y-label")
+
+  // Draw wall with hatching
+  on-layer(
+    1, // draw wall above pressure lines
+    rect(
+      (0, 0),
+      (wall-width, 3.6),
+      fill: hatched,
+      pattern: "north-east-lines",
+      stroke: 0.75pt,
+    ),
+  )
+
+  // Draw potential curves
+  let samples = 100
+  let dx = (6 - wall-width) / samples
+
+  // First curve (blue)
+  let (A1, B1, alpha1) = (10, 25, 1)
+
+  for ii in range(samples - 1) {
+    let x1 = wall-width + ii * dx
+    let x2 = x1 + dx
+    let y1 = lennard-jones(x1, A1, B1, alpha1)
+    let y2 = lennard-jones(x2, A1, B1, alpha1)
+    line(
+      (x1, y1),
+      (x2, y2),
+      stroke: blue,
+    )
+  }
+  content((4.2, -0.6), text(fill: blue)[$1 / alpha << ell$], name: "alpha-label")
+
+  // Second curve (orange)
+  let (A2, B2, alpha2) = (15, 120, 3)
+
+  for ii in range(samples - 1) {
+    let x1 = wall-width + ii * dx
+    let x2 = x1 + dx
+    let y1 = lennard-jones(x1, A2, B2, alpha2)
+    let y2 = lennard-jones(x2, A2, B2, alpha2)
+    line(
+      (x1, y1),
+      (x2, y2),
+      stroke: orange,
+      name: "orange-line-" + str(ii),
+    )
+  }
+  content((4.2, 0.4), text(fill: orange)[$1 / alpha << ell$], name: "alpha-label")
+})

assets/wall/wall.yml → assets/gas-pressure-on-wall/gas-pressure-on-wall.yml

@@ -1,4 +1,4 @@
-title: Wall
+title: Gas Pressure on Wall
 tags:
   - physics
   - thermodynamics

assets/qft-propagators/qft-propagators.typ

@@ -0,0 +1,100 @@
+#import "@preview/cetz:0.3.2": canvas, draw, decorations
+#import draw: line, content, circle
+
+#set page(width: auto, height: auto, margin: 5pt)
+
+#let re-range = 5
+#let im-range = 4
+#let arrow-style = (end: "stealth", fill: black, scale: 0.5)
+
+#canvas({
+  // Axes
+  // Real axis with zigzag decoration
+  // TODO: add arrow at the end, requireshttps://github.com/cetz-package/cetz/issues/446
+  decorations.zigzag(
+    line(
+      (-re-range, 0),
+      (re-range, 0),
+    ),
+    amplitude: 0.1,
+    segment-length: 0.2,
+    name: "x-axis",
+    mark: arrow-style,
+  )
+  content(
+    "x-axis.end",
+    $"Re"(omega)$,
+    anchor: "north-east",
+    padding: (top: 5pt),
+  )
+
+  // Imaginary axis
+  line(
+    (0, -im-range + 1),
+    (0, im-range - 1),
+    mark: arrow-style,
+    name: "y-axis",
+  )
+  content(
+    "y-axis.end",
+    $"Im"(omega)$,
+    anchor: "north-west",
+    padding: (left: 5pt),
+  )
+
+  // Matsubara frequencies
+  for n in range(-im-range, im-range + 1) {
+    circle(
+      (0, 2 / 3 * n),
+      radius: 0.05,
+      fill: black,
+      name: "omega" + str(n),
+    )
+  }
+  content(
+    (-1.1, 2),
+    align(right)[Matsubara\ frequencies],
+  )
+
+  // Propagators
+  // Advanced propagator (red)
+  line(
+    (-re-range, -1),
+    (re-range, -1),
+    stroke: (paint: red, dash: "dashed"),
+    name: "advanced",
+  )
+  content(
+    (rel: (0, -0.4), to: "advanced.start"),
+    text(red)[advanced],
+    anchor: "south-west",
+    padding: (left: 5pt),
+  )
+
+  // Retarded propagator (blue)
+  line(
+    (-re-range, 1),
+    (re-range, 1),
+    stroke: (paint: blue, dash: "dashed"),
+    name: "retarded",
+  )
+  content(
+    "retarded.start",
+    text(blue)[retarded],
+    anchor: "south-west",
+    padding: 2pt,
+  )
+
+  // Feynman propagator (orange)
+  line(
+    (-re-range, -1),
+    (re-range, 1),
+    stroke: (paint: orange, dash: "dashed"),
+    name: "feynman",
+  )
+  content(
+    (rel: (-0.7, -0.55), to: "feynman.end"),
+    text(orange)[Feynman],
+    padding: 2pt,
+  )
+})

assets/propagators/propagators.yml → assets/qft-propagators/qft-propagators.yml

@@ -1,6 +1,9 @@
-title: Propagators
+title: QFT Propagators
 tags:
   - physics
   - quantum field theory
   - Matsubara
+  - causality
+  - Green's function
+  - Feynman
 description: null