BEC-002
Harmonic Interacting
SuccessfulScratch27 Sept 2026 · 211 ms
main
73fafa8596
Code diff
vs BEC-001--- a/experiments/harmonic-reference.json
+++ b/experiments/harmonic-interacting.json
@@ -1 +1 @@
-{"experiment":"harmonic-ground-state","method":"split-step","g":0,"dt":0.01,"nx":256,"xmax":8,"trap":"harmonic"}+{"experiment":"harmonic-ground-state","method":"split-step","g":1,"dt":0.01,"nx":256,"xmax":8,"trap":"harmonic"}Scientific diff
vs BEC-001Ground-state energy
changed0.499877 ℏω→0.6894037 ℏωΔ 0.1895267
solver.energy · results/harmonic-interacting/summary.json#/energy
Chemical potential
changed0.499877 ℏω→0.8699416 ℏωΔ 0.3700646
solver.chemical_potential · results/harmonic-interacting/summary.json#/chemical_potential
Interaction strength g
changed0 dimensionless→1 dimensionlessΔ 1
solver.interaction_strength · command
Iterations
changed2 →444 Δ 442
solver.iterations · results/harmonic-interacting/summary.json#/iterations
Normalization error
changed4.440892e-16 →0 Δ -4.440892e-16
solver.normalization_error · results/harmonic-interacting/summary.json#/normalization_error
Stationary-equation residual
changed0.0004018658 →0.0005514652 Δ 0.0001495994
solver.stationary_residual · results/harmonic-interacting/summary.json#/residual
Energy error from E = 1/2
removed-0.0001229891 ℏω
solver.harmonic_reference_energy_error · derived: solver.energy minus 0.5 for g = 0 harmonic reference
Chemical-potential error from μ = 1/2
removed-0.0001229891 ℏω
solver.harmonic_reference_mu_error · derived: solver.chemical_potential minus 0.5 for g = 0 harmonic reference
Interpretation
What the result means
At fixed harmonic trap, dt, and grid, increasing g from 0 to 1 changes E from 0.499877011 to 0.689403720 ℏω and μ from 0.499877011 to 0.869941623 ℏω. This is the computed repulsive-interaction case; the differences are relative to the non-interacting reference, not a convergence estimate.
Computed with the 1D Gross-Pitaevskii solver (split-step, g=1, dt=0.01).
Outputs
Artefacts
Ground-state density
figure · results/harmonic-interacting/density.png
Open artefact ↗
Energy convergence
figure · results/harmonic-interacting/convergence.png
Open artefact ↗Loading preview…
Solver summary
data · results/harmonic-interacting/summary.json
Open artefact ↗Structured evidence
Facts
| Fact | Value | Source |
|---|---|---|
Ground-state energy★ Uncategorised / solver.energy | 0.6894037 ℏω | results/harmonic-interacting/summary.json#/energy |
Grid half-width Uncategorised / grid.half_width | 8 aₕₒ | command |
Grid points Uncategorised / grid.points | 256 | command |
Chemical potential Uncategorised / solver.chemical_potential | 0.8699416 ℏω | results/harmonic-interacting/summary.json#/chemical_potential |
Imaginary-time step Uncategorised / solver.imaginary_time_step | 0.01 ω⁻¹ | command |
Interaction strength g Uncategorised / solver.interaction_strength | 1 dimensionless | command |
Iterations Uncategorised / solver.iterations | 444 | results/harmonic-interacting/summary.json#/iterations |
Imaginary-time method Uncategorised / solver.method | split-step | command |
Normalization error Uncategorised / solver.normalization_error | 0 | results/harmonic-interacting/summary.json#/normalization_error |
Stationary-equation residual Uncategorised / solver.stationary_residual | 0.0005514652 | results/harmonic-interacting/summary.json#/residual |
Trap potential Uncategorised / trap.type | harmonic | command |
Execution
Logs
stdout
No stdout was captured.
stderr
No stderr was captured.