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A Study of the Bohm-de Broglie Potential in Plasmas A Quantum-Hydrodynamic Exploration of Collective Effects, Nonlocality, and Wave- Particle Duality in Ionized Media

Ijaz Durrani

Published Jan 1, 2026• 0 citations
Publisher
DOI
10.13140/rg.2.2.28333.86247

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Signaling by a delayed-choice experimental setup was discussed in the previous report [M. Sato, quant-ph/0409059]. In this report, the speed of the interference pattern generation in Wheeler's delayed-choice experiment is discussed, and a feasible experimental proposal is provided. The duality of locality and nonlocality obviously appears in the de Broglie-Bohm picture. Locality corresponds to the particle property and nonlocality corresponds to the wave property. The interference of a photon can be recognized using the de Broglie-Bohm picture. A photon moves at the speed of light, however the speed of the interference pattern formation, which is conducted by a quantum potential, is not seen to be restricted by the speed of light.
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In this research we study the effect of matter-wave instability on electron beam transport with arbitrary degree of degeneracy. Particular class of solutions of the Schrödinger-Poisson system is used to model the electron-beam transport at constant speed. It is shown that such electron-beam is described by a coupled driven pseudoforce system solution of which leads to plasmon excitations with dual wave-particle character. The fundamental quantum mechanical de Broglie relation is found to be due to the resonant interaction of particle-like plasmon excitation branch with the electron beam drift. We further obtain a generalized double lengthscale de Broglie wave-particle relation through which various beam-plasmon instability is studied in this model. The quantum charge screening and the chemical potential effects on the matter-wave formation and instabilities are discussed in detail and the well-known Aharonov-Bohm effect is revisited in current quantum hydrodynamic model. Current research may further illuminate the origin of matter-wave in quantum mechanics and lead to clear understanding of novel wave-particle interactions.