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

On Hypothetical Factors Limiting the Operation of Nanoelectronic Devices: the Zitterbewegung

Alexander V. Gritsunov, И. Н. Бондаренко, А. Г. Пащенко, O. Yu. Babychenko, Gennady Bendeberya, Володимир Карнаушенко

Published Oct 8, 2024• 0 citations
Publisher

Abstract

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.

DOI
10.1109/tcset64720.2024.10755925

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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.
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.
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.
The Assessment of the interpretation of Zitterbewegung for free particle solution using various models has been carried out in this work where we firstly considered by using the free particle solution for which Dirac equation and projection operator were carried out.. ln this case, it was invariably revealed that the solution have two doubly degenerate eigenvalues representing positive and negative state that was further support by the analysis which was carried out using Heisenberg’s equation and the representation in relativistic velocity and semi-classical equation of motion for acceleration., but in this second case, the results obtained were observed to have two terms, first terms standing in for rapidly oscillatory motion and the second term representing average motion of the particle in x-direction. The first term in the expression is the one deemed to signify zitterbewegung which is one considered to be sas a result of the fluctuation resulting from the interference between negative and positive energy state while the other term is the normal state terms signifying the average motion of the particle. This therefore confirms the explicit nature of using Dirac equation in handling problems involving the behavior of free particles in field as compared to the use of semiclassical equation of motion.
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.
Zitterbewegung (ZBW), the trembling motion predicted by the Dirac equation, has long remained unobservable in free electrons due to its sub-Compton scale. We elaborately construct a relativistic vortex electron wave packet as a coherent superposition of both positive- and negative-energy Dirac states and derive their space-time dynamics. Our analysis demonstrates that introducing orbital angular momentum provides a mechanism for amplifying the ZBW amplitude far beyond that of conventional Gaussian packets, while maintaining coherence. The resulting relativistic vortex states unify Gaussian and Bessel-Gaussian models within a single framework and opens new possibilities for observing relativistic quantum dynamics in structured electron wave packets.
In the Dirac theory for the motion of free relativistic electrons, highly oscillatory components appear in the time evolution of physical observables such as position, velocity, and spin angular momentum. This effect is known as zitterbewegung. We present a theoretical analysis of rather different Hamiltonians with gapped and/or spin-split energy spectrum (including the Rashba, Luttinger, and Kane Hamiltonians) that exhibit analogs of zitterbewegung as a common feature. We find that the amplitude of oscillations of the Heisenberg velocity operator v(t)\mathbf{v}(t)v(t) generally equals the uncertainty for a simultaneous measurement of two linearly independent components of v\mathbf{v}v. It is also shown that many features of zitterbewegung are shared by the simple and well-known Landau Hamiltonian, describing the dynamics of two-dimensional (2D) electron systems in the presence of a magnetic field perpendicular to the plane. Finally, we also discuss the oscillatory dynamics of 2D electrons arising from the interplay of Rashba spin splitting and a perpendicular magnetic field.