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.
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.
In this work the root to macroscopic quantum effects is revealed based on the quasiparticle model of collective excitations in an arbitrary degenerate electron gas. The N-electron quantum system is considered as N streams coupled, through the Poisson's relation, which are localized in momentum space rather than electron localization in real space, assumed in ordinary many body theories. Using a new wavefunction representation, the N+1-coupled system is reduced to simple pseudoforce equations via quasiparticle (collective quantum) model leading to a generalized matter wave dispersion relation. It is shown that the resulting dual lengthscale de Broglie's matter wave theory predicts macroscopic quantum effects and deterministic field trajectories for charges moving in the electron gas due to the coupling of the electrostatic field to the local electron number density. It is remarked that any quantum many body system composed of large number of interacting particles acts as a dual arm device controlling the microscopic single particle effects with one hand and the macroscopic phenomena with the other. Current analysis can be further extended to include the magnetic potential and spin exchange effects. Present model can also be used to confirm macroscopic entanglement of charged particles embedded in a quantum electron fluid.
We revisit de Broglie’s double-solution pilot-wave theory in light of insights gained from the hydrodynamic pilot-wave system discovered by Couder and Fort [1]. de Broglie proposed that quantum particles are characterized by an internal oscillation at the Compton frequency, at which rest mass energy is exchanged with field energy. He further proposed that the resulting pilot-wave field satisfies the Klein–Gordon equation. While he developed a guidance equation for the particle, he did not specify how the particle generates the wave. Informed by the hydrodynamic pilot-wave system, we explore a variant of de Broglie’s mechanics in which the form of the Compton-scale dynamic interaction between particle and pilot wave is specified. The particle is modeled as a localized periodic disturbance of the Klein–Gordon field at twice the Compton frequency. We simulate the evolution of the particle position by assuming that the particle is propelled by the local gradient of its pilot wave field. Resonance is achieved between the particle and its pilot wave, leading to self-excited motion of the particle. The particle locks into quasi-steady motion characterized by a mean momentum p ¯ = ℏ k , where k is the wavenumber of the surrounding matter waves. Speed modulations along the particle path arise with the de Broglie wavelength and frequency c k . The emergent dynamics is strongly reminiscent of that arising in the hydrodynamic pilot-wave system, on the basis of which we anticipate the emergence of quantum statistics in various settings. Our results suggest the potential value of a new hydrodynamically-inspired pilot-wave theory for the motion of quantum particles.
Maxwell matter waves emerge from a perspective, complementary to de Broglie's, that matter is fundamentally a wave phenomenon whose particle aspects are revealed by quantum mechanics. Their quantum mechanical description is derived through the introduction of a matter vector potential, having frequency ω0, to Schrodinger's equation for a massive particle. Maxwell matter waves are then seen to be coherent excitations of a single-mode of the matter-wave field. In the classical regime, their mechanics is captured by a matter analog of Maxwell's equations for the electromagnetic field. As such, Maxwell matter waves enable a spectrum of systems that have useful optical analogs, such as resonant matter-wave interferometric sensors and matter-wave parametric oscillators. These waves are associated with a wavelength that is tied to the drive frequency ω0 rather than to the massive particle's energy, as is ordinarily the case with de Broglie matter waves. As a result, simple interferometric measurements lead to different outcomes for the two types of waves. While their apparent departure from de Broglie character is surprising, Maxwell matter waves are wholly consistent with quantum mechanics.
Abstract We present a classical hydrodynamic analog of free relativistic quantum particles inspired by de Broglie's pilot wave theory and recent developments in hydrodynamic quantum analogs. The proposed model couples a periodically forced Klein-Gordon equation with a nonrelativistic particle dynamic equation. The coupled equations may represent both quantum particles and classical particles driven by the gradients of locally excited Faraday waves. Exact stationary solutions of the coupled system reveal a highly nonlinear mechanism responsible for the self-propulsion of free particles, leading to the onset of unsteady motion. Although the model is essentially nonrelativistic, a stabilizing mechanism for any particle traveling close to the wave signaling speed emerges through the coupling with the wavefield. Consequently, inline particle oscillations comparable to de Broglie's wavelength formula are realized through this fully-classical model, suggesting a new classical interpretation for the motion of relativistic quantum particles.
To address the theoretical gap in traditional de Broglie wave theory that fails to clarify the physical excitation mechanism of matter waves, this paper proposes the de Broglie Wave-Virtual Photon Exchange Synchronization Law and reveals the intrinsic physical origin of de Broglie matter waves from the perspective of virtual photon exchange. Based on well-recognized physical formulas including the de Broglie energy-frequency relation, the relativistic energy-momentum relation, and the core equations of quantum electrodynamics (QED), this paper carries out rigorous quantitative derivation and obtains the de Broglie Wave-Virtual Photon Exchange Synchronization Formula , which describes the relation between virtual photon exchange and the evolution of de Broglie waves. Physical analysis of the formula shows that the de Broglie matter wave is not an intrinsic and spontaneous property of particles, but a dynamic wave effect directly excited by momentum exchange between virtual photons and particles in electromagnetic interaction. The frequency, wavelength, and wave properties of the de Broglie wave are uniquely determined by the intensity and frequency of virtual photon exchange, and the two sets of physical quantities maintain strict synchronization during physical evolution. In addition, this paper clarifies the velocity-dependent modulation effect of virtual photon exchange on de Broglie waves: the modulation effect is weak at low velocities, becomes significant at high velocities, and the key wave parameters (frequency, momentum correlation) of de Broglie waves and virtual photons achieve quantitative unification as the particle velocity approaches the speed of light. This theory establishes a rigorous, quantitative, and unified relation between the virtual photon exchange mechanism and the origin of de Broglie waves, improves the physical interpretation of matter wave origin, and provides a new theoretical perspective for the study of wave-particle duality and electromagnetic interaction of microscopic particles.
From a Newtonian-Maxwellian solution for a perturbed vacuum with a physical structure constructed based on pivotal experimental observations, we have achieved a general scheme for the formation of basic material particles. A basic particle, which may be e.g. an electron, is composed of a tiny free aether-pole (a bare charge) and the mechanical wave disturbances -- identifying with electromagnetic waves -- generated by it in the medium. When in motion, as a result of a first kind source effect, this particle wave exhibits all of wave and dynamic properties known for a de Broglie wave, and is here called a Newton- de Broglie (NdB) particle wave. In a confined space, the Newtonian solution for the NdB particle wave is equivalent to that given by Schrodinger's quantum mechanics. Through this general scheme we have accomplished a basic task of the unification of the classical- and the quantum- mechanics, both in terms of the deduction of the latter from the former, and the convergence of the latter into the former at high velocities. Through completing the task, we unfold the origins of a series of phenomena including the electromagnetic waves, the electromagnetic radiation and absorption, atomic and thermal excitations, the inertial mass, the Schrodinger's wavefunction and de Broglie wave, the Heisenberg's uncertainty relation, the de Broglie relations, the simultaneous existence of electron and positron or generally of particles and their anti-particles, the (rest) mass-energy equivalence relation, etc. The general scheme facilitates also a Theory of Relative Motion which we present in a separate paper, II; a series of followed studies are planned. (An original report of the scheme with a Preface remarking on the changes in later publications.)