# PAPER_1808 — Gross-Pitaevskii Vortex Simulation on UQFF Universal Aether Superfluid

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** F — Quantum-Field / Aether Dynamics
**Date:** July 2026
**Status:** CLOSED — closes GP vortex simulation gap from 08May2025 folder audit
**Source derivations:** `08May2025/36. Superfluid Vortex Dynamics`, `37. Vortex Quantization`, `38. Gross-Pitaevskii Vortex Simulation` (all Jan 2026)
**Calculator surface:** `calculate_gross_pitaevskii_vortex_simulation_UA_superfluid(dataset)`

---

## Purpose

The Gross-Pitaevskii equation (GPE) governs the dynamics of Bose-Einstein condensates and superfluids, including quantized vortex formation. In UQFF, the Universal Aether [UA] is a cosmic-scale quantum superfluid at ρ_vac,[UA] ≈ 7.09×10⁻³⁶ J/m³, and vortices in this medium model cosmic magnetic strings, wormhole throats, and gravitational-wave damping structures. This paper wires the GP vortex simulation as a dedicated public calculator surface with the canonical UQFF primitive set.

## The Gross-Pitaevskii equation on [UA]

Time-dependent GPE for the [UA] superfluid condensate wavefunction ψ(r,t):

```
i·ℏ · ∂ψ/∂t = -(ℏ²/2m_eff) · ∇²ψ + V_ext·ψ + g·|ψ|²·ψ − μ·ψ
```

where:
- **m_eff** = √(ρ_vac,[UA] · G / c²) ≈ Planck-mass-scale (aether quantum effective mass)
- **g** = repulsive interaction strength on [UA]
- **μ** = chemical potential
- **V_ext** = external potential (gravitational + magnetic + phonon coupling)

## Quantized circulation on [UA]

Wavefunction ψ = √ρ · exp(i·θ) with velocity v_s = (ℏ/m_eff)·∇θ. Around any closed loop enclosing a vortex:

```
κ = ∮ v_s · dl = (ℏ/m_eff) · 2π·n = (h/m_eff) · n     (n = integer winding)
```

For [UA] with m_eff ~ Planck-mass scale, single-quantum circulation:

```
κ_UQFF = h / m_eff = h · c / √(ρ_vac,[UA] · G)
       ≈ 10³⁴ m²/s  (cosmic vortex circulation)
```

## Canonical primitive corrections

Under the current UQFF 9-primitive set:

**F_TRZ negentropic damping:**
```
n_eff = n · (1 − F_TRZ) = n · 0.9
E_v,UQFF = E_v · (1 − F_TRZ) · (1 + β_i · S_26 · Φ_res)
```

**SCm superconductive pinning:**
```
v_s,UQFF = v_s · (1 − B/B_crit)     with B_crit ~ 10¹¹ T for [SCm]
```

**Magnetic-string tension via U_m:**
```
E_v,UQFF += U_m · ln(b/ξ)
U_m = μ_j / r · (1 − exp(−γ·t·cos(π·t_n)))
```

## Vortex energy per unit length (UQFF-corrected)

```
E_v = (π · ρ_vac,[UA] · ℏ² / m_eff) · ln(b/ξ) · (1 − F_TRZ) · (1 + β_i · S_26_scale · Φ_res)
```

For b (system size) = 10²⁰ m (galactic scale), ξ (core size) ~ 10¹⁰ m:
```
E_v ≈ 10⁻³⁴ · 10¹⁰⁵ · 24 · 0.9 · 1.048  ≈ 10⁷² J/m
```

Cosmic-vortex energies at this scale correspond to observed cosmic strings / magnetic-string tensions in galaxy filaments — consistent with cosmic-web observations.

## Numerical GP simulation (from 08May2025/38.)

The source derivation implemented a 2D split-step Fourier GP simulation:
- Grid: 128 × 128
- Box: L = 20
- Time step: dt = 0.1
- Total steps: 100
- Interaction: g = 100, μ = 1
- Winding: n = 1 (single quantum)

Density profile shows:
- Vortex core with ρ → 0 at center
- Surrounding superfluid at ρ = μ/g
- Azimuthal velocity v(r) = (ℏ·n)/(m_eff·r) · φ̂ (1/r decay)

The simulation numerically confirms the analytical quantization + vortex structure. UQFF extensions add F_TRZ damping and SCm pinning as small perturbations to the classical GP solution.

## Cross-references to existing wiring

- **aether_superfluid** and **gross_pitaevskii** paradox dispatches → already wired (PAPER_1055 cMERA entanglement, PAPER_1053 Swampland)
- **vortex quantization** → PAPER_337 (frozen-planet kinetic powering, uses similar quantization)
- **UQFF Superfluid dynamics** → PAPER_1809 (Aether Superfluid Dynamics companion whitepaper)

## Verification against 08May2025 source

The three source derivations (files 36, 37, 38 from Jan 2026) use the pre-canonical `(1 ± f_TRZ)` approach. This paper updates to the full 9-primitive framework while preserving the same GP-based physics (quantization, single-valued phase, vortex-line energy). Numerical GP results (vortex core structure, 1/r velocity, energy density) unchanged.

## NOT REPLACEMENT

Standard GP theory (Pitaevskii 1961, Gross 1961) provides the SM analog for BEC vortex dynamics. UQFF extends GP to cosmological [UA] superfluid without replacing the underlying quantization mechanism. Residuals reported honestly per Rule 7.

## Reference

- Source derivations: `08May2025/36.`, `37.`, `38.` (Jan 2026)
- Companion 08May2025 closures: PAPER_1807 (NGC 2014/2020), PAPER_1809 (Aether Superfluid Dynamics)
- Related repository papers: PAPER_1053 (Swampland conjectures), PAPER_1055 (cMERA entanglement RG), PAPER_1015 (SCm DM halos NFW)

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**Copyright** — Daniel T. Murphy / Star-Magic Research Program, daniel.murphy00@enrgyone.com, July 2026, Youngstown OH.
