BEC-004
Gradient Flow
SuccessfulNotable27 Sept 2026 · 212 ms
main
73fafa8596
Code diff
vs BEC-002--- a/experiments/harmonic-interacting.json
+++ b/experiments/gradient-flow.json
@@ -1 +1 @@
-{"experiment":"harmonic-ground-state","method":"split-step","g":1,"dt":0.01,"nx":256,"xmax":8,"trap":"harmonic"}+{"experiment":"harmonic-ground-state","method":"gradient-flow","g":1,"dt":0.01,"nx":256,"xmax":8,"trap":"harmonic"}Scientific diff
vs BEC-002Ground-state energy
changed0.6894037 ℏω→0.6894043 ℏωΔ 5.431416e-7
solver.energy · results/gradient-flow/summary.json#/energy
Chemical potential
changed0.8699416 ℏω→0.8700337 ℏωΔ 0.00009208365
solver.chemical_potential · results/gradient-flow/summary.json#/chemical_potential
Iterations
changed444 →187 Δ -257
solver.iterations · results/gradient-flow/summary.json#/iterations
Imaginary-time method
changedsplit-step →gradient-flow
solver.method · command
Normalization error
changed0 →2.220446e-16 Δ 2.220446e-16
solver.normalization_error · results/gradient-flow/summary.json#/normalization_error
Stationary-equation residual
changed0.0005514652 →0.001220579 Δ 0.0006691143
solver.stationary_residual · results/gradient-flow/summary.json#/residual
Interpretation
What the result means
At the same harmonic potential, g, dt, and grid, gradient flow gives E=0.689404263 ℏω versus 0.689403720 ℏω for split-step, an absolute difference of 5.43e-07 ℏω. The energies agree within 1×10⁻⁵ ℏω; the finite-difference residual (0.00122) is higher than the split-step residual (0.000551), so residuals retain method-dependent discretization.
Computed with the 1D Gross-Pitaevskii solver (gradient-flow, g=1, dt=0.01).
Outputs
Artefacts
Ground-state density
figure · results/gradient-flow/density.png
Open artefact ↗
Energy convergence
figure · results/gradient-flow/convergence.png
Open artefact ↗Loading preview…
Solver summary
data · results/gradient-flow/summary.json
Open artefact ↗Structured evidence
Facts
| Fact | Value | Source |
|---|---|---|
Ground-state energy★ Uncategorised / solver.energy | 0.6894043 ℏω | results/gradient-flow/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 | 0.8700337 ℏω | results/gradient-flow/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 | 187 | results/gradient-flow/summary.json#/iterations |
Imaginary-time method Uncategorised / solver.method | gradient-flow | command |
Normalization error Uncategorised / solver.normalization_error | 2.220446e-16 | results/gradient-flow/summary.json#/normalization_error |
Stationary-equation residual Uncategorised / solver.stationary_residual | 0.001220579 | results/gradient-flow/summary.json#/residual |
Trap potential Uncategorised / trap.type | harmonic | command |
Execution
Logs
stdout
No stdout was captured.
stderr
No stderr was captured.