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The Davis-Landau Sonic Onset Law: Universal Critical Velocity for Vortex Nucleation in Bose-Einstein Condensates

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Main Author:	Davis, Bee Rosa
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Published:	Zenodo 2026
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author	Davis, Bee Rosa
author_facet	Davis, Bee Rosa
contents	<p>We report the discovery of a universal critical velocity law for obstacle-nucleated vortex shedding in quantum fluids—the <strong>Davis-Landau Sonic Onset Law</strong>:</p> <p><span><span><span>vc=cs/3v_c = c_s / \sqrt{3}</span><span><span><span><span>v</span><span><span><span><span><span><span><span>c</span></span></span></span><span></span></span></span></span></span><span>=</span></span><span><span><span>c</span><span><span><span><span><span><span><span>s</span></span></span></span><span></span></span></span></span></span><span>/</span><span><span><span><span><span><span><span>3</span></span></span></span><span></span></span></span></span></span></span></span></span></p> <p>where <span><span>cs=μ/mc_s = \sqrt{\mu/m} </span><span><span><span><span>c</span><span><span><span><span><span><span><span>s</span></span></span></span><span></span></span></span></span></span><span>=</span></span><span><span><span><span><span><span><span><span>μ</span><span>/</span><span>m</span></span></span></span><span></span></span></span></span></span></span></span> is the speed of sound. Through GPU-accelerated Gross-Pitaevskii simulations validated against experimental measurements, we establish that the dimensionless ratio <span><span>β=vc/cs=1/3≈0.5774\beta = v_c/c_s = 1/\sqrt{3} \approx 0.5774 </span><span><span><span>β</span><span>=</span></span><span><span><span>v</span><span><span><span><span><span><span><span>c</span></span></span></span><span></span></span></span></span></span><span>/</span><span><span>c</span><span><span><span><span><span><span><span>s</span></span></span></span><span></span></span></span></span></span><span>=</span></span><span><span>1/</span><span><span><span><span><span><span><span>3</span></span></span></span><span></span></span></span></span><span>≈</span></span><span><span>0.5774</span></span></span></span> is a <strong>geometric invariant</strong>—independent of atomic species, interaction strength, and obstacle geometry.</p> <p><strong>Key Results:</strong></p> <ol> <li><strong>Universal Prefactor</strong>: The ratio <span><span>β=vc/cs=0.5785±0.0002\beta = v_c/c_s = 0.5785 \pm 0.0002 </span><span><span><span>β</span><span>=</span></span><span><span><span>v</span><span><span><span><span><span><span><span>c</span></span></span></span><span></span></span></span></span></span><span>/</span><span><span>c</span><span><span><span><span><span><span><span>s</span></span></span></span><span></span></span></span></span></span><span>=</span></span><span><span>0.5785</span><span>±</span></span><span><span>0.0002</span></span></span></span> is identical across ⁸⁷Rb, ²³Na, and ⁷Li, matching <span><span>1/31/\sqrt{3} </span><span><span><span>1/</span><span><span><span><span><span><span><span>3</span></span></span></span><span></span></span></span></span></span></span></span> to within 0.2%. These species span a mass ratio of 12 :1.</li> <li><strong>Obstacle Independence</strong>: Critical velocity shows zero dependence on obstacle size for <span><span>σ/ξ∈[2,5]\sigma/\xi \in [2, 5] </span><span><span><span>σ</span><span>/</span><span>ξ</span><span>∈</span></span><span><span>[</span><span>2</span><span>,</span><span>5</span><span>]</span></span></span></span> (spread = 1.00×), confirming <span><span>vcv_c </span><span><span><span><span>v</span><span><span><span><span><span><span><span>c</span></span></span></span><span></span></span></span></span></span></span></span></span> is an intrinsic superfluid property.</li> <li><strong>Experimental Agreement</strong>: All predictions fall within 2σ of published measurements, including independent ⁴He validation using neutron scattering roton parameters.</li> <li><strong>Sonic Onset Mechanism</strong>: Vortices nucleate when local Mach number <span><span>Mmax⁡=1M_{\max} = 1 </span><span><span><span><span>M</span><span><span><span><span><span><span><span><span><span>m</span><span>a</span><span>x</span></span></span></span></span></span><span></span></span></span></span></span><span>=</span></span><span><span>1</span></span></span></span> at the obstacle rim. The factor <span><span>3\sqrt{3} </span><span><span><span><span><span><span><span><span><span>3</span></span></span></span><span></span></span></span></span></span></span></span> is the flow amplification for smooth repulsive obstacles—a geometric constant.</li> </ol> <p><strong>Relation to Prior Work:</strong></p> <p>This paper extends the Davis Framework for geometric physics, connecting to:</p> <ul> <li><em>The Incompressibility of Topological Charge</em> (Yang-Mills Mass Gap) — DOI: 10.5281/zenodo.17846521</li> <li><em>Holonomy-First Navier-Stokes Regularity</em> — DOI: 10.5281/zenodo.18216597</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> <p><strong>Keywords:</strong> Bose-Einstein condensate, critical velocity, superfluidity, Gross-Pitaevskii equation, vortex nucleation, Landau criterion, sonic onset, geometric invariant, Davis Field Equations, quantum hydrodynamics</p> <p><strong>License:</strong> Creative Commons Attribution 4.0 International (CC BY 4.0)</p> <p><strong>Related Identifiers:</strong></p> <ul> <li>References: DOI 10.5281/zenodo.17846521 (Yang-Mills Mass Gap)</li> <li>References: DOI 10.5281/zenodo.18216597 (Navier-Stokes Regularity)</li> </ul>
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id	zenodo_https___doi_org_10_5281_zenodo_18343936
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publishDate	2026
publisher	Zenodo
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spellingShingle	The Davis-Landau Sonic Onset Law: Universal Critical Velocity for Vortex Nucleation in Bose-Einstein Condensates Davis, Bee Rosa <p>We report the discovery of a universal critical velocity law for obstacle-nucleated vortex shedding in quantum fluids—the <strong>Davis-Landau Sonic Onset Law</strong>:</p> <p><span><span><span>vc=cs/3v_c = c_s / \sqrt{3}</span><span><span><span><span>v</span><span><span><span><span><span><span><span>c</span></span></span></span><span></span></span></span></span></span><span>=</span></span><span><span><span>c</span><span><span><span><span><span><span><span>s</span></span></span></span><span></span></span></span></span></span><span>/</span><span><span><span><span><span><span><span>3</span></span></span></span><span></span></span></span></span></span></span></span></span></p> <p>where <span><span>cs=μ/mc_s = \sqrt{\mu/m} </span><span><span><span><span>c</span><span><span><span><span><span><span><span>s</span></span></span></span><span></span></span></span></span></span><span>=</span></span><span><span><span><span><span><span><span><span>μ</span><span>/</span><span>m</span></span></span></span><span></span></span></span></span></span></span></span> is the speed of sound. Through GPU-accelerated Gross-Pitaevskii simulations validated against experimental measurements, we establish that the dimensionless ratio <span><span>β=vc/cs=1/3≈0.5774\beta = v_c/c_s = 1/\sqrt{3} \approx 0.5774 </span><span><span><span>β</span><span>=</span></span><span><span><span>v</span><span><span><span><span><span><span><span>c</span></span></span></span><span></span></span></span></span></span><span>/</span><span><span>c</span><span><span><span><span><span><span><span>s</span></span></span></span><span></span></span></span></span></span><span>=</span></span><span><span>1/</span><span><span><span><span><span><span><span>3</span></span></span></span><span></span></span></span></span><span>≈</span></span><span><span>0.5774</span></span></span></span> is a <strong>geometric invariant</strong>—independent of atomic species, interaction strength, and obstacle geometry.</p> <p><strong>Key Results:</strong></p> <ol> <li><strong>Universal Prefactor</strong>: The ratio <span><span>β=vc/cs=0.5785±0.0002\beta = v_c/c_s = 0.5785 \pm 0.0002 </span><span><span><span>β</span><span>=</span></span><span><span><span>v</span><span><span><span><span><span><span><span>c</span></span></span></span><span></span></span></span></span></span><span>/</span><span><span>c</span><span><span><span><span><span><span><span>s</span></span></span></span><span></span></span></span></span></span><span>=</span></span><span><span>0.5785</span><span>±</span></span><span><span>0.0002</span></span></span></span> is identical across ⁸⁷Rb, ²³Na, and ⁷Li, matching <span><span>1/31/\sqrt{3} </span><span><span><span>1/</span><span><span><span><span><span><span><span>3</span></span></span></span><span></span></span></span></span></span></span></span> to within 0.2%. These species span a mass ratio of 12 :1.</li> <li><strong>Obstacle Independence</strong>: Critical velocity shows zero dependence on obstacle size for <span><span>σ/ξ∈[2,5]\sigma/\xi \in [2, 5] </span><span><span><span>σ</span><span>/</span><span>ξ</span><span>∈</span></span><span><span>[</span><span>2</span><span>,</span><span>5</span><span>]</span></span></span></span> (spread = 1.00×), confirming <span><span>vcv_c </span><span><span><span><span>v</span><span><span><span><span><span><span><span>c</span></span></span></span><span></span></span></span></span></span></span></span></span> is an intrinsic superfluid property.</li> <li><strong>Experimental Agreement</strong>: All predictions fall within 2σ of published measurements, including independent ⁴He validation using neutron scattering roton parameters.</li> <li><strong>Sonic Onset Mechanism</strong>: Vortices nucleate when local Mach number <span><span>Mmax⁡=1M_{\max} = 1 </span><span><span><span><span>M</span><span><span><span><span><span><span><span><span><span>m</span><span>a</span><span>x</span></span></span></span></span></span><span></span></span></span></span></span><span>=</span></span><span><span>1</span></span></span></span> at the obstacle rim. The factor <span><span>3\sqrt{3} </span><span><span><span><span><span><span><span><span><span>3</span></span></span></span><span></span></span></span></span></span></span></span> is the flow amplification for smooth repulsive obstacles—a geometric constant.</li> </ol> <p><strong>Relation to Prior Work:</strong></p> <p>This paper extends the Davis Framework for geometric physics, connecting to:</p> <ul> <li><em>The Incompressibility of Topological Charge</em> (Yang-Mills Mass Gap) — DOI: 10.5281/zenodo.17846521</li> <li><em>Holonomy-First Navier-Stokes Regularity</em> — DOI: 10.5281/zenodo.18216597</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> <p><strong>Keywords:</strong> Bose-Einstein condensate, critical velocity, superfluidity, Gross-Pitaevskii equation, vortex nucleation, Landau criterion, sonic onset, geometric invariant, Davis Field Equations, quantum hydrodynamics</p> <p><strong>License:</strong> Creative Commons Attribution 4.0 International (CC BY 4.0)</p> <p><strong>Related Identifiers:</strong></p> <ul> <li>References: DOI 10.5281/zenodo.17846521 (Yang-Mills Mass Gap)</li> <li>References: DOI 10.5281/zenodo.18216597 (Navier-Stokes Regularity)</li> </ul>
title	The Davis-Landau Sonic Onset Law: Universal Critical Velocity for Vortex Nucleation in Bose-Einstein Condensates
url	https://doi.org/10.5281/zenodo.18343936