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BEC Ground State

Computed runs from the public BEC Ground State example. Explore scientific results, code changes, and provenance.

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Weekly team report

Week 39

BEC Ground State · 2026-W39

Scientific results
BEC-003 →Baseline

Harmonic Small Step

Summary

Computed with the 1D Gross-Pitaevskii solver (split-step, g=1, dt=0.005).

Interpretation

Reducing dt from 0.01 to 0.005 changes E by 7.92e-08 ℏω (0.689403720 to 0.689403641 ℏω). The change is below 1×10⁻⁶ ℏω at fixed g, trap, and grid, supporting this run as the harmonic reference baseline.

Figures

Ground-state density
Ground-state density
results/harmonic-small-step/density.png
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Energy convergence
Energy convergence
results/harmonic-small-step/convergence.png
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Highlighted scientific changes

Compared with BEC-002

Ground-state energychanged
0.6894037 ℏω→0.6894036 ℏωΔ -7.923768e-8
BEC-004 →Notable

Gradient Flow

Summary

Computed with the 1D Gross-Pitaevskii solver (gradient-flow, g=1, dt=0.01).

Interpretation

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.

Figures

Ground-state density
Ground-state density
results/gradient-flow/density.png
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Energy convergence
Energy convergence
results/gradient-flow/convergence.png
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Highlighted scientific changes

Compared with BEC-002

Ground-state energychanged
0.6894037 ℏω→0.6894043 ℏωΔ 5.431416e-7
BEC-001 →Notable

Harmonic Reference

Summary

Computed with the 1D Gross-Pitaevskii solver (split-step, g=0, dt=0.01).

Interpretation

For the non-interacting harmonic reference, E=0.499877011 ℏω and μ=0.499877011 ℏω. The computed absolute errors from 1/2 are 0.000123 and 0.000123 ℏω, consistent with the finite-grid discretization at nx=256.

Figures

Ground-state density
Ground-state density
results/harmonic-reference/density.png
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Energy convergence
Energy convergence
results/harmonic-reference/convergence.png
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Highlighted scientific changes

First run in this experiment

Ground-state energyadded
0.499877 ℏω