docs: add "KB vs HB method" example to documentation (#436)

Author: oameye

docs/pages.jl

@@ -21,6 +21,7 @@ pages = [
         "Ab Initio Noise spectrum" => "examples/ab_initio_noise.md",
         "Adiabatic sweep" => "examples/steady_state_sweep.md",
         "Quantum Cumulants" => "examples/cumulants_KPO.md",
+        "KB vs HB method" => "examples/harmonic_oscillator_KB_vs_HB.md",
         ],
     ],
     "Resources" => [

examples/harmonic_oscillator_KB_vs_HB.jl

@@ -23,9 +23,10 @@ harmonic_eq = rearrange_standard(harmonic_eq)
 
 varied = (ω => range(0.1, 1.9, 200)) # range of parameter values
 fixed = (ω0 => 1.0, γ => 0.05, F => 0.1) # fixed parameters
-result_krylov1 = get_steady_states(krylov_eq1, varied, fixed)
-result_krylov2 = get_steady_states(krylov_eq2, varied, fixed)
-result_harmonic = get_steady_states(harmonic_eq, varied, fixed);
+show_progress = false # show progress bar
+result_krylov1 = get_steady_states(krylov_eq1, varied, fixed; show_progress)
+result_krylov2 = get_steady_states(krylov_eq2, varied, fixed; show_progress)
+result_harmonic = get_steady_states(harmonic_eq, varied, fixed; show_progress);
 
 #
 
@@ -74,7 +75,11 @@ plot(
     ),
     plot_linear_response(
         result_harmonic, x, 1; Ω_range=range(0.1, 1.9, 200), title="Harmonic"
+    ),
+    plot_linear_response(
+        result_harmonic, x, 1; Ω_range=range(0.1, 1.9, 200), title="Exact", order=2
     );
-    layout=(3, 1),
+    layout=(4, 1),
     clims=(0, 250),
+    size=(800, 600),
 )