Quantum Particle-Quantized Fluid Theory: A Discrete Lagrangian Approach to Turbulence and Vortex Quantization
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| Formato: | Recurso digital |
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2025
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| _version_ | 1866901353295511552 |
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| author | Lee, Byoungwoo |
| author_facet | Lee, Byoungwoo |
| contents | <p>This theoretical proposal introduces a novel quantum fluid framework that re-conceptualizes fluid dynamics beyond the classical continuum assumption. Addressing the limitations of the Navier-Stokes equations at micro- and nano-scales, and inspired by phenomena observed in quantum fluids like superfluid helium II and Bose-Einstein condensates, this theory posits that fluid motion can be described by a discrete Lagrangian<sup></sup>.</p> <p>The core of this framework lies in two fundamental concepts:</p> <div></div> <p></p> <ul> <li><strong>Minimal Volume Elements (<span><span><span><span>Δ</span><span><span>V</span><span><span><span><span><span><span><span><span>min</span></span></span></span></span><span></span></span></span></span></span></span></span></span>):</strong> Defined as the smallest fluid volume where continuum assumptions break down, typically comparable to the molecular mean free path<sup></sup>. Within these elements, fluid behavior is treated as discrete clusters rather than a continuous medium<sup></sup>.</li> <li> <div></div> <strong>Quantized Circulation (<span><span><span><span>Γ<span><span><span><span><span><span><span>0</span></span></span></span><span></span></span></span></span></span></span></span></span>):</strong> We hypothesize that at sufficiently small scales, fluid elements carry a discrete circulation quantum, analogous to the quantized vortices observed in superfluids (<span><span><span><span>Γ<span><span><span><span><span><span><span>0</span></span></span></span><span></span></span></span></span></span><span>=</span></span><span><span>n</span><span>h</span><span>/</span><span>m</span><span>,</span><span>n</span><span>∈</span></span><span><span>Z</span></span></span></span>)<sup></sup>. This extends the concept of vortex quantization from quantum fluids to potentially classical fluids at micro-scales<sup></sup>. <div></div> </li> </ul> <p>A discrete Lagrangian is formulated for these minimal volume elements, incorporating a quantum pressure term derived from a Madelung-type decomposition<sup></sup>. Importantly, the theory models vortex creation and annihilation not as continuous processes, but as stochastic quantum events governed by a probability function (<span><span><span><span><span>P</span><span><span><span><span><span><span><span><span>ev</span></span></span></span></span><span></span></span></span></span></span><span>(</span><span>Γ<span><span><span><span><span><span><span>0</span></span></span></span><span></span></span></span></span></span><span>)</span><span>∝</span></span><span><span><span>e</span><span><span><span><span><span><span><span>−Δ<span>E</span>/<span>k</span><span><span><span>B</span></span><span></span></span><span>T</span></span></span></span></span></span></span></span></span></span></span></span>)<sup></sup>.</p> <p>This approach aims to provide new insights into: </p> <p><strong>Turbulence Spectra:</strong> By interpreting deviations from the Kolmogorov <span><span><span><span><span>k</span><span><span><span><span><span><span><span>−5/3</span></span></span></span></span></span></span></span></span></span></span> spectrum through discrete, quantized vortex fusion and fission events. </p> <ul> <li><strong>Micro-Scale Dissipation:</strong> Quantifying energy absorption and emission at molecular scales<sup></sup>.</li> <li> <div></div> <strong>Fundamental Fluid Dynamics:</strong> Offering a unified framework for understanding micro-scale discontinuities and energy dissipation in various fluid regimes, from nano-fluidics to superfluids and plasmas<sup></sup>. <div></div> </li> </ul> <p>Numerical schemes (SPH-Quantum, LBM-Quantum) are proposed for implementation, leveraging n-body acceleration techniques<sup></sup>. Validation will involve comparisons with classical Couette and Poiseuille flows, as well as experimental data from superfluid helium II rotation, focusing on vortex density, circulation distribution, and critical angular velocity<sup></sup>.</p> <p>This work represents a foundational step towards a more comprehensive understanding of fluid dynamics at the interface of classical and quantum mechanics.</p> <p></p> <p></p> <p></p> <p></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15518757 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Quantum Particle-Quantized Fluid Theory: A Discrete Lagrangian Approach to Turbulence and Vortex Quantization Lee, Byoungwoo Quantum Fluid Dynamics, Discrete Lagrangian, Navier-Stokes Equations, Turbulence, Vortex Quantization, Superfluidity, Bose-Einstein Condensate, Madelung Transform, Quantum Pressure, Smoothed Particle Hydrodynamics (SPH), Lattice Boltzmann Method (LBM), Nano-fluidics, Micro-fluidics, Energy Cascade, Fluid Mechanics <p>This theoretical proposal introduces a novel quantum fluid framework that re-conceptualizes fluid dynamics beyond the classical continuum assumption. Addressing the limitations of the Navier-Stokes equations at micro- and nano-scales, and inspired by phenomena observed in quantum fluids like superfluid helium II and Bose-Einstein condensates, this theory posits that fluid motion can be described by a discrete Lagrangian<sup></sup>.</p> <p>The core of this framework lies in two fundamental concepts:</p> <div></div> <p></p> <ul> <li><strong>Minimal Volume Elements (<span><span><span><span>Δ</span><span><span>V</span><span><span><span><span><span><span><span><span>min</span></span></span></span></span><span></span></span></span></span></span></span></span></span>):</strong> Defined as the smallest fluid volume where continuum assumptions break down, typically comparable to the molecular mean free path<sup></sup>. Within these elements, fluid behavior is treated as discrete clusters rather than a continuous medium<sup></sup>.</li> <li> <div></div> <strong>Quantized Circulation (<span><span><span><span>Γ<span><span><span><span><span><span><span>0</span></span></span></span><span></span></span></span></span></span></span></span></span>):</strong> We hypothesize that at sufficiently small scales, fluid elements carry a discrete circulation quantum, analogous to the quantized vortices observed in superfluids (<span><span><span><span>Γ<span><span><span><span><span><span><span>0</span></span></span></span><span></span></span></span></span></span><span>=</span></span><span><span>n</span><span>h</span><span>/</span><span>m</span><span>,</span><span>n</span><span>∈</span></span><span><span>Z</span></span></span></span>)<sup></sup>. This extends the concept of vortex quantization from quantum fluids to potentially classical fluids at micro-scales<sup></sup>. <div></div> </li> </ul> <p>A discrete Lagrangian is formulated for these minimal volume elements, incorporating a quantum pressure term derived from a Madelung-type decomposition<sup></sup>. Importantly, the theory models vortex creation and annihilation not as continuous processes, but as stochastic quantum events governed by a probability function (<span><span><span><span><span>P</span><span><span><span><span><span><span><span><span>ev</span></span></span></span></span><span></span></span></span></span></span><span>(</span><span>Γ<span><span><span><span><span><span><span>0</span></span></span></span><span></span></span></span></span></span><span>)</span><span>∝</span></span><span><span><span>e</span><span><span><span><span><span><span><span>−Δ<span>E</span>/<span>k</span><span><span><span>B</span></span><span></span></span><span>T</span></span></span></span></span></span></span></span></span></span></span></span>)<sup></sup>.</p> <p>This approach aims to provide new insights into: </p> <p><strong>Turbulence Spectra:</strong> By interpreting deviations from the Kolmogorov <span><span><span><span><span>k</span><span><span><span><span><span><span><span>−5/3</span></span></span></span></span></span></span></span></span></span></span> spectrum through discrete, quantized vortex fusion and fission events. </p> <ul> <li><strong>Micro-Scale Dissipation:</strong> Quantifying energy absorption and emission at molecular scales<sup></sup>.</li> <li> <div></div> <strong>Fundamental Fluid Dynamics:</strong> Offering a unified framework for understanding micro-scale discontinuities and energy dissipation in various fluid regimes, from nano-fluidics to superfluids and plasmas<sup></sup>. <div></div> </li> </ul> <p>Numerical schemes (SPH-Quantum, LBM-Quantum) are proposed for implementation, leveraging n-body acceleration techniques<sup></sup>. Validation will involve comparisons with classical Couette and Poiseuille flows, as well as experimental data from superfluid helium II rotation, focusing on vortex density, circulation distribution, and critical angular velocity<sup></sup>.</p> <p>This work represents a foundational step towards a more comprehensive understanding of fluid dynamics at the interface of classical and quantum mechanics.</p> <p></p> <p></p> <p></p> <p></p> |
| title | Quantum Particle-Quantized Fluid Theory: A Discrete Lagrangian Approach to Turbulence and Vortex Quantization |
| topic | Quantum Fluid Dynamics, Discrete Lagrangian, Navier-Stokes Equations, Turbulence, Vortex Quantization, Superfluidity, Bose-Einstein Condensate, Madelung Transform, Quantum Pressure, Smoothed Particle Hydrodynamics (SPH), Lattice Boltzmann Method (LBM), Nano-fluidics, Micro-fluidics, Energy Cascade, Fluid Mechanics |
| url | https://doi.org/10.5281/zenodo.15518757 |