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IEEE International Conference on Advanced Trends in Radioelectronics, Telecommunications and Computer Engineering (TCSET)

Theory of natural oscillatory systems and advance in nanoelectronics

Alexander V. Gritsunov, И. Н. Бондаренко, А. Г. Пащенко, O. Yu. Babychenko

Published Feb 1, 2018• 6 citations
Publisher

Abstract

Specific treatments of some quantum phenomena substantial for progress in nanotechnology and nanoelectronics are presented. De Broglie waves are interpreted as oscillations of the generalized coordinates of natural oscillatory systems with distributed parameters (NOSs). The spatio-temporal localization of the NOS wave packets and Heisenberg's uncertainty principle both are assumed to be results of the stochastic exchange with action quanta between different NOSs. The quantum kinematics (spatio-temporal evolution of NOS wave packets), quantum dynamics (interaction by means of random exchange with momentum-energy quanta between wave packets of different NOSs), and quantum statistics (probability laws for the stochastic exchange with action quanta between the wave packets in the Minkowski spacetime) are discussed. Both the action four-scalar and the momentum-energy four-vector, as the directional How of action through 3D world, are assimilated with the geometry of NOS eigenmodes in the Minkowski spacetime. The conservation law for the action is supposed as a necessary condition for the energy-momentum conservation. The simplest examples of NOS wave packets are given. Some outcomes of application of this theory to solid-state phenomena are discussed.

DOI
10.1109/tcset.2018.8336230

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Specific treatments of some quantum phenomena substantial for progress in nanotechnology and nanoelectronics are presented. De Broglie waves are interpreted as oscillations of the generalized coordinates of natural oscillatory systems with distributed parameters (NOSs). The spatio-temporal localization of the NOS wave packets and Heisenberg's uncertainty principle both are assumed to be results of the stochastic exchange with action quanta between different NOSs. The quantum kinematics (spatio-temporal evolution of NOS wave packets), quantum dynamics (interaction by means of random exchange with momentum-energy quanta between wave packets of different NOSs), and quantum statistics (probability laws for the stochastic exchange with action quanta between the wave packets in the Minkowski spacetime) are discussed. Both the action four-scalar and the momentum-energy four-vector, as the directional How of action through 3D world, are assimilated with the geometry of NOS eigenmodes in the Minkowski spacetime. The conservation law for the action is supposed as a necessary condition for the energy-momentum conservation. The simplest examples of NOS wave packets are given. Some outcomes of application of this theory to solid-state phenomena are discussed.
Statistical dependences of quantum phenomena substantial for advance in nanoelectronic technology are discussed basing on the interpretation of de Broglie matter waves as real oscillations of the generalized coordinates of some natural oscillatory systems with distributed parameters (NOSs). E.g., electrons are supposed to be excited wave packets of natural electron-positron oscillatory system (NEPOS), not hard particles; photons are wave packets of natural electromagnetic oscillatory system (NEMOS) and so on. The Wheeler-Feynman's concept of “direct interparticle action” is developed for both the quantum radiation-absorption and the Coulomb interaction. The spatio-temporal localization of the NOS wave packets and Heisenberg's “uncertainty principle” both are supposed to be results of the permanent stochastic exchange with action quanta between different NOSs (e.g., NEPOS and NEMOS) according to the general laws of the statistical physics. The basic principles of quantum statistics (probability laws for the stochastic exchange with action quanta between the wave packets of NEPOS and NEMOS in the Minkowski spacetime) are discussed. The new physical sense of de Broglie wavefunctions is illustrated with the simplest quantum systems. E.g., “free electron” is presumed as a spatially localized area (within its “interval of uncertainty”) filled with “pink noise” of NEPOS oscillations. The finite probability of harmonics with large spatial wavenumbers in spectra of NEPOS and NEMOS “wide” wavepackets makes scattering of high-energy electrons still possible creating outward appearance of “point particles” existence.
Fundamental issues of quantum electrodynamics of nanophotonic systems essential for further progress of nanotechnology are considered. Hypothesis of natural oscillatory systems with distributed parameters (NOSs) as bases for “real”, not “probabilistic”, de Broglie matter waves underlies the theory of natural oscillatory systems (TNOS). TNOS is a 4D theory in essence; the action, not momentum-energy, is regarded as a primary conservative and quantized physical value of Universe causing excitation of NOSs. Conservation laws individually for the positive and the negative parts of action are supposed. The spatial localization of fermion NOS wave packets (“particles”) and Heisenberg's uncertainty principle both are supposed to be results of a stochastic “spread” of fermion NOS action over multiple degrees of freedom of boson NOSs (according to the general laws of statistical physics). The physical origin of both Coulomb potential and own (spin) magnetic moment of fermions is considered to be also the action spread over boson NOS. A 4D spatio-temporal structure of fermion wave packet conjointly with estimation of actions of respective “forced” eigenmodes of boson NOS (virtual photons) is the subject of this paper.
A statistical method for the quantization of natural electromagnetic (NEMOS) and electron-positron (NEPOS) oscillatory systems is discussed. The Wheeler-Feynman's concept of “direct interparticle action” for the quantum radiation-absorption is generalized to the Coulomb interaction. The energy-momentum conservation is postulated as a fundamental law forbidding any objective their “uncertainty”. The spatial (spatio-temporal) localization of NEPOS wavepackets and the Heisenberg's “uncertainty principle” are supposed to be a result of a permanent interaction of NEPOS and NEMOS, i.e., the stochastic exchange with random quanta of momentum (or energy-momentum) between ones. The absence of “zero-point oscillations” of the natural oscillatory systems is asserted. The new physical sense of De Broglie wavefunctions is illustrated with the simplest quantum systems “electrons in potential wells”.
Fundamental issues of quantum electrodynamics of nanoelectronic systems essential for further progress of nanotechnology are considered. The zitterbewegung is a hypothetical rapid oscillatory motion of elementary particles (specifically, electrons) that obey relativistic wave equations. Those oscillations (with double rest energy of the fermion) have a place between the positive and negative energy states of the wave packet. Along with other relativistic effects of the quantum field theory (the Lamb shift, the Casimir effect and so on), the zitterbewegung might be a factor making worsen noise characteristics of prospective nanoelectronic devices or limiting possible new constructive solutions in nanotechnology. In defiance of known conclusions of the Copenhagen school, operating with complex wavefunctions, the theory of natural oscillatory systems (TNOS) deals with four-vector analytic-signal wavefunctions having single-side (e.g., nonnegative definite) spectra in the time domain. This allows consider only positive energies for fermions, thus taking away acuteness of the problem until its definitive clarification in experimental way.
An attempt is made to generalize the basic idea of the self-sufficient potential formalism in electrodynamics (interpretation of electromagnetic phenomena as natural or forced oscillations of the Minkowski spacetime treated as a distributed electromagnetic oscillating system) on the De Broglie waves. Both electrons and positrons are considered as excited modes (oscillations) of a distributed electron-positron oscillating system, not as “hard” particles. Thus, the matter waves are treated as real oscillations of the Minkowski spacetime, not as Born's “probability waves”.
Wave-particle duality is widely regarded as one of the conceptual pillars of modern quantum theory, providing the framework through which the behavior of microscopic matter can be consistently interpreted. According to this principle, microscopic entities such as electrons, photons, atoms and even complex molecules exhibit both wave-like and particle-like properties depending on the experimental configuration used to observe them. This duality is quantitatively formalized through the De Broglie relation, which associates a wavelength with any particle possessing momentum. The present work provides a comprehensive theoretical analysis of the physical and mathematical foundations of wave-particle duality, focusing particularly on the De Broglie wavelength and the kinetic energy of the electron in both non-relativistic and relativistic regimes. The connection between the De Broglie hypothesis and Schrödinger’s equation is discussed in detail, highlighting the role of the kinetic energy operator and the interpretation of matter waves in terms of quantum wave packets. Experimental evidence supporting the wave nature of matter, including electron diffraction experiments and interferometry techniques, is also reviewed. Beyond their conceptual importance, these principles underpin several modern technologies, including electron microscopy, nanoscale semiconductor devices and quantum metrology. The analysis demonstrates that the De Broglie relation provides a unifying framework connecting momentum, wavelength and kinetic energy, thereby forming a fundamental bridge between classical mechanics, quantum theory and modern technological applications.