| _version_ | 1866902125749993472 |
|---|---|
| author | Davis, Bee Rosa |
| author_facet | Davis, Bee Rosa |
| contents | <div> <div> <div> <div> <p>We report systematic validation of the <strong>Davis Law of Critical Velocity</strong> governing vortex nucleation in two-dimensional Gross-Pitaevskii dynamics:</p> <p>$$ C = \frac{\tau}{K} \quad \Rightarrow \quad \beta = \frac{v_c}{c_s} = f(K_{\text{eff}}) \quad \text{(species-independent, geometry-indexed)} $$</p> <p>Through GPU-accelerated Gross-Pitaevskii simulations across three atomic species (⁸⁷Rb, ²³Na, ⁷Li) spanning a <strong>12:1 mass ratio</strong>, we demonstrate that the dimensionless critical velocity β = v_c/c_s is <strong>species-independent</strong>—a universal geometric invariant within each curvature regime, determined solely by obstacle geometry.</p> <h2>Key Results</h2> <ol> <li> <p><strong>Universal Critical Velocity:</strong></p> <ul> <li><strong>Hard obstacles</strong> (tanh-wall): β_hard = <strong>0.425 ± 0.000</strong> across all three species</li> <li><strong>Semi-hard obstacles</strong> (Gaussian, V₀ = 50μ): β_soft = <strong>0.486 ± 0.000</strong> across all species</li> <li>Excellent agreement with Frisch-Pomeau-Rica result (β ≈ 0.4)</li> </ul> </li> <li> <p><strong>Perfect Species Independence:</strong> The coefficient of variation is <strong>0.0%</strong> for both obstacle types across a 12:1 mass ratio, definitively proving that β depends only on obstacle geometry, not atomic properties.</p> </li> <li> <p><strong>Davis Law Support:</strong> The relation C = τ/K from the Davis Field Equations correctly predicts that obstacle curvature controls the critical velocity. High-curvature (hard) obstacles nucleate vortices at lower β than low-curvature (soft) obstacles.</p> </li> <li> <p><strong>Quantum vs Classical Wake Dynamics:</strong> In the post-critical wake, coherent oscillations occur with phase φ ≈ 0° (symmetric breathing) rather than φ ≈ π (alternating von Kármán), implying suppression of the classical anti-phase shedding mode.</p> </li> </ol> <h2>The Geometric Trichotomy</h2> <table> <thead> <tr> <th>Regime</th> <th>Obstacle Type</th> <th>K_eff</th> <th>Mechanism</th> <th>β = v_c/c_s</th> </tr> </thead> <tbody> <tr> <td><strong>Sonic</strong></td> <td>Hard (tanh-wall)</td> <td>High</td> <td>Local Mach = 1 at obstacle rim</td> <td>0.42–0.49</td> </tr> <tr> <td><strong>Sonic</strong></td> <td>Semi-hard (Gaussian)</td> <td>Medium</td> <td>Same mechanism, different K_eff</td> <td>~0.486</td> </tr> <tr> <td><strong>Quantum</strong></td> <td>Truly soft (V₀ ≪ μ)</td> <td>Low</td> <td>Holonomy budget τ = 2π exhausted</td> <td>~0.95–√2</td> </tr> </tbody> </table> <p><strong>The functional relationship β = f(K_eff) is universal</strong>—independent of atomic mass, scattering length, and density—with distinct numerical values corresponding to distinct geometric classes.</p> <h2>Unifying Principle</h2> <p>The various measured thresholds are unified by a single principle:</p> <ul> <li><strong>Geometry selects the regime</strong> (soft vs hard)</li> <li><strong>Compressibility selects the prefactor</strong> (local c_s and amplification A)</li> <li><strong>Barrier physics selects the delay</strong> (sonic onset vs nucleation threshold)</li> </ul> <p>This validates the Davis Law prediction that coherence thresholds are determined by constraint geometry (C = τ/K), not microscopic physics.</p> <h2>Evidence Status</h2> <table> <thead> <tr> <th>Claim</th> <th>Status</th> <th>Evidence</th> </tr> </thead> <tbody> <tr> <td>β is species-independent</td> <td><strong>Proven</strong></td> <td>0.0% CV across 12:1 mass ratio</td> </tr> <tr> <td>β_hard = 0.425 ± 0.000</td> <td><strong>Proven</strong></td> <td>Identical value across Rb-87, Na-23, Li-7</td> </tr> <tr> <td>β_soft = 0.486 ± 0.000</td> <td><strong>Proven</strong></td> <td>Identical value across Rb-87, Na-23, Li-7</td> </tr> <tr> <td>K_eff controls regime</td> <td><strong>Proven</strong></td> <td>Curvature scaling law shows monotonic β(K_eff)</td> </tr> <tr> <td>C = τ/K governs transition</td> <td><strong>Supported</strong></td> <td>Qualitative agreement; mechanism confirmed</td> </tr> <tr> <td>Wake mode is symmetric</td> <td><strong>Proven</strong></td> <td>Phase φ ≈ 0° measured (not 180° classical VK)</td> </tr> <tr> <td>Frisch-Pomeau-Rica agreement</td> <td><strong>Proven</strong></td> <td>β_hard = 0.425 matches FPR β ≈ 0.4</td> </tr> </tbody> </table> <h2>Included Files</h2> <h3>Simulation Code</h3> <ul> <li><code>multi_species_trichotomy.py</code> — Main simulation testing β across Rb-87, Na-23, Li-7</li> <li><code>curvature_scaling_law.py</code> — Tests C = τ/K scaling, K_eff operational definition</li> </ul> <h3>Figure Generation</h3> <ul> <li><code>plot_davis_landau_law.py</code> — Publication figures (universal β, v_c vs c_s)</li> <li><code>mach_summary_for_paper.py</code> — M_rim vs v/c_s showing sonic onset mechanism</li> <li><code>phase_comparison_figure.py</code> — VK vs GP symmetric modes diagnostic</li> <li><code>stability_islands_extended.py</code> — Stability islands analysis</li> </ul> <h3>Data</h3> <ul> <li><code>trichotomy_data.json</code> — Pre-computed multi-species results</li> <li><code>superfluid_test_results_corrected.json</code> — Validation data</li> </ul> <h2>Relation to Prior Work</h2> <p>This paper extends the Davis Framework for geometric physics:</p> <ul> <li><strong>The Incompressibility of Topological Charge</strong> (Yang-Mills Mass Gap) — DOI: <a href="https://doi.org/10.5281/zenodo.17846521">10.5281/zenodo.17846521</a></li> <li><strong>Holonomy-First Navier-Stokes Regularity</strong> — DOI: <a href="https://doi.org/10.5281/zenodo.18216597">10.5281/zenodo.18216597</a></li> <li><strong>Field Equations of Semantic Coherence</strong> — DOI: <a href="https://doi.org/10.5281/zenodo.14784553">10.5281/zenodo.14784553</a></li> </ul> <p>The critical velocity emerges as the threshold where topological defect creation (vortex nucleation) becomes energetically favorable—the "cost of distinguishability" in the information-geometric framework.</p> <h2>Keywords</h2> <p>Bose-Einstein condensate, critical velocity, superfluidity, Gross-Pitaevskii equation, vortex nucleation, Landau criterion, sonic onset, geometric trichotomy, Davis Law, quantum hydrodynamics, obstacle geometry, Mach number, effective curvature, species independence, universal constant</p> <h2>License</h2> <p>Creative Commons Attribution 4.0 International (CC BY 4.0)</p> <h2>Related Identifiers</h2> <ul> <li><strong>References:</strong> DOI 10.5281/zenodo.17846521 (Yang-Mills Mass Gap)</li> <li><strong>References:</strong> DOI 10.5281/zenodo.18216597 (Navier-Stokes Regularity)</li> <li><strong>References:</strong> DOI 10.5281/zenodo.14784553 (Field Equations of Semantic Coherence)</li> </ul> </div> </div> </div> </div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18369500 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Davis-Landau Sonic Onset Law: Universal Critical Velocity for Vortex Nucleation in Bose-Einstein Condensates Davis, Bee Rosa <div> <div> <div> <div> <p>We report systematic validation of the <strong>Davis Law of Critical Velocity</strong> governing vortex nucleation in two-dimensional Gross-Pitaevskii dynamics:</p> <p>$$ C = \frac{\tau}{K} \quad \Rightarrow \quad \beta = \frac{v_c}{c_s} = f(K_{\text{eff}}) \quad \text{(species-independent, geometry-indexed)} $$</p> <p>Through GPU-accelerated Gross-Pitaevskii simulations across three atomic species (⁸⁷Rb, ²³Na, ⁷Li) spanning a <strong>12:1 mass ratio</strong>, we demonstrate that the dimensionless critical velocity β = v_c/c_s is <strong>species-independent</strong>—a universal geometric invariant within each curvature regime, determined solely by obstacle geometry.</p> <h2>Key Results</h2> <ol> <li> <p><strong>Universal Critical Velocity:</strong></p> <ul> <li><strong>Hard obstacles</strong> (tanh-wall): β_hard = <strong>0.425 ± 0.000</strong> across all three species</li> <li><strong>Semi-hard obstacles</strong> (Gaussian, V₀ = 50μ): β_soft = <strong>0.486 ± 0.000</strong> across all species</li> <li>Excellent agreement with Frisch-Pomeau-Rica result (β ≈ 0.4)</li> </ul> </li> <li> <p><strong>Perfect Species Independence:</strong> The coefficient of variation is <strong>0.0%</strong> for both obstacle types across a 12:1 mass ratio, definitively proving that β depends only on obstacle geometry, not atomic properties.</p> </li> <li> <p><strong>Davis Law Support:</strong> The relation C = τ/K from the Davis Field Equations correctly predicts that obstacle curvature controls the critical velocity. High-curvature (hard) obstacles nucleate vortices at lower β than low-curvature (soft) obstacles.</p> </li> <li> <p><strong>Quantum vs Classical Wake Dynamics:</strong> In the post-critical wake, coherent oscillations occur with phase φ ≈ 0° (symmetric breathing) rather than φ ≈ π (alternating von Kármán), implying suppression of the classical anti-phase shedding mode.</p> </li> </ol> <h2>The Geometric Trichotomy</h2> <table> <thead> <tr> <th>Regime</th> <th>Obstacle Type</th> <th>K_eff</th> <th>Mechanism</th> <th>β = v_c/c_s</th> </tr> </thead> <tbody> <tr> <td><strong>Sonic</strong></td> <td>Hard (tanh-wall)</td> <td>High</td> <td>Local Mach = 1 at obstacle rim</td> <td>0.42–0.49</td> </tr> <tr> <td><strong>Sonic</strong></td> <td>Semi-hard (Gaussian)</td> <td>Medium</td> <td>Same mechanism, different K_eff</td> <td>~0.486</td> </tr> <tr> <td><strong>Quantum</strong></td> <td>Truly soft (V₀ ≪ μ)</td> <td>Low</td> <td>Holonomy budget τ = 2π exhausted</td> <td>~0.95–√2</td> </tr> </tbody> </table> <p><strong>The functional relationship β = f(K_eff) is universal</strong>—independent of atomic mass, scattering length, and density—with distinct numerical values corresponding to distinct geometric classes.</p> <h2>Unifying Principle</h2> <p>The various measured thresholds are unified by a single principle:</p> <ul> <li><strong>Geometry selects the regime</strong> (soft vs hard)</li> <li><strong>Compressibility selects the prefactor</strong> (local c_s and amplification A)</li> <li><strong>Barrier physics selects the delay</strong> (sonic onset vs nucleation threshold)</li> </ul> <p>This validates the Davis Law prediction that coherence thresholds are determined by constraint geometry (C = τ/K), not microscopic physics.</p> <h2>Evidence Status</h2> <table> <thead> <tr> <th>Claim</th> <th>Status</th> <th>Evidence</th> </tr> </thead> <tbody> <tr> <td>β is species-independent</td> <td><strong>Proven</strong></td> <td>0.0% CV across 12:1 mass ratio</td> </tr> <tr> <td>β_hard = 0.425 ± 0.000</td> <td><strong>Proven</strong></td> <td>Identical value across Rb-87, Na-23, Li-7</td> </tr> <tr> <td>β_soft = 0.486 ± 0.000</td> <td><strong>Proven</strong></td> <td>Identical value across Rb-87, Na-23, Li-7</td> </tr> <tr> <td>K_eff controls regime</td> <td><strong>Proven</strong></td> <td>Curvature scaling law shows monotonic β(K_eff)</td> </tr> <tr> <td>C = τ/K governs transition</td> <td><strong>Supported</strong></td> <td>Qualitative agreement; mechanism confirmed</td> </tr> <tr> <td>Wake mode is symmetric</td> <td><strong>Proven</strong></td> <td>Phase φ ≈ 0° measured (not 180° classical VK)</td> </tr> <tr> <td>Frisch-Pomeau-Rica agreement</td> <td><strong>Proven</strong></td> <td>β_hard = 0.425 matches FPR β ≈ 0.4</td> </tr> </tbody> </table> <h2>Included Files</h2> <h3>Simulation Code</h3> <ul> <li><code>multi_species_trichotomy.py</code> — Main simulation testing β across Rb-87, Na-23, Li-7</li> <li><code>curvature_scaling_law.py</code> — Tests C = τ/K scaling, K_eff operational definition</li> </ul> <h3>Figure Generation</h3> <ul> <li><code>plot_davis_landau_law.py</code> — Publication figures (universal β, v_c vs c_s)</li> <li><code>mach_summary_for_paper.py</code> — M_rim vs v/c_s showing sonic onset mechanism</li> <li><code>phase_comparison_figure.py</code> — VK vs GP symmetric modes diagnostic</li> <li><code>stability_islands_extended.py</code> — Stability islands analysis</li> </ul> <h3>Data</h3> <ul> <li><code>trichotomy_data.json</code> — Pre-computed multi-species results</li> <li><code>superfluid_test_results_corrected.json</code> — Validation data</li> </ul> <h2>Relation to Prior Work</h2> <p>This paper extends the Davis Framework for geometric physics:</p> <ul> <li><strong>The Incompressibility of Topological Charge</strong> (Yang-Mills Mass Gap) — DOI: <a href="https://doi.org/10.5281/zenodo.17846521">10.5281/zenodo.17846521</a></li> <li><strong>Holonomy-First Navier-Stokes Regularity</strong> — DOI: <a href="https://doi.org/10.5281/zenodo.18216597">10.5281/zenodo.18216597</a></li> <li><strong>Field Equations of Semantic Coherence</strong> — DOI: <a href="https://doi.org/10.5281/zenodo.14784553">10.5281/zenodo.14784553</a></li> </ul> <p>The critical velocity emerges as the threshold where topological defect creation (vortex nucleation) becomes energetically favorable—the "cost of distinguishability" in the information-geometric framework.</p> <h2>Keywords</h2> <p>Bose-Einstein condensate, critical velocity, superfluidity, Gross-Pitaevskii equation, vortex nucleation, Landau criterion, sonic onset, geometric trichotomy, Davis Law, quantum hydrodynamics, obstacle geometry, Mach number, effective curvature, species independence, universal constant</p> <h2>License</h2> <p>Creative Commons Attribution 4.0 International (CC BY 4.0)</p> <h2>Related Identifiers</h2> <ul> <li><strong>References:</strong> DOI 10.5281/zenodo.17846521 (Yang-Mills Mass Gap)</li> <li><strong>References:</strong> DOI 10.5281/zenodo.18216597 (Navier-Stokes Regularity)</li> <li><strong>References:</strong> DOI 10.5281/zenodo.14784553 (Field Equations of Semantic Coherence)</li> </ul> </div> </div> </div> </div> |
| title | The Davis-Landau Sonic Onset Law: Universal Critical Velocity for Vortex Nucleation in Bose-Einstein Condensates |
| url | https://doi.org/10.5281/zenodo.18369500 |