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It has recently been claimed that Zitterbewegung has been observed. However, we argue that it is not an observable and that the authors' observations must be reinterpreted.

In this paper, we present an approximate analytic solution to the Dirac equation in the Schwarzschild geometry to investigate the Zitterbewegung (ZB) effect. The analytical expression for the current density, which is induced by the motion of a wave packet of electrons, is obtained. In addition, the intensity of dipole radiation near the black hole is calculated. The proposed approach is based on the Schrödinger representation, thereby allowing to consider the ZB effect in the case of a curved space. The considered example demonstrates a possibility for applying this approach to astrophysical applications, in particular to problems of the electron radiation in the vicinity of real black holes.

In this paper, we investigate the trembling motion effect in the cosmic spacetime. The cosmic string was considered to be charged and carrying a magnetic flow. Zitterbewegung (ZB) is calculated based on the Dirac equation in the curved spacetime. An analytic expression for the electric current is obtained and analyzed.

We study the classical dynamics of nonrelativistic particles endowed with spin. Nonvanishing Zitterbewegung terms appear in the equation of motion also in the small momentum limit. We derive a generalized work-energy theorem which suggests classical interpretations for tunnel effect and quantum potential.

A self-adjoint dynamical time operator is introduced in Dirac's relativistic formulation of quantum mechanics and shown to satisfy a commutation relation with the Hamiltonian analogous to that of the position and momentum operators. The ensuing time-energy uncertainty relation involves the uncertainty in the instant of time when the wave packet passes a particular spatial position and the energy uncertainty associated with the wave packet at the same time, as envisaged originally by Bohr. The instantaneous rate of change of the position expectation value with respect to the simultaneous expectation value of the dynamical time operator is shown to be the phase velocity, in agreement with de Broglie's hypothesis of a particle associated wave whose phase velocity is larger than c. Thus, these two elements of the original basis and interpretation of quantum mechanics are integrated into its formal mathematical structure. Pauli's objection is shown to be resolved or circumvented. Possible relevance to current developments in electron channeling, in interference in time, in Zitterbewegung-like effects in spintronics, graphene and superconducting systems and in cosmology is noted.

We have considered the effects of space and momentum noncommutativity separately on the zitterbewegung (ZBW) phenomenon. In the space noncommutativity scenario, it has been expressed that, due to the conservation of momentum, the Fourier decomposition of the expectation value of position does not change. However, the noncommutative (NC) space corrections to the magnetic dipole moment of electron, that was traditionally perceived to come into play only in the first-order of perturbation theory, appear in the leading-order calculations with the similar structure and numerically the same order, but with an opposite sign. This result may explain why for large lumps of masses, the Zeeman effect due to the noncommutativity remains undetectable. Moreover, we have shown that the x- and y-components of the electron magnetic dipole moment, contrary to the commutative (usual) version, are nonzero and with the same structure as the z-component. In the momentum noncommutativity case, we have indicated that, due to the relevant external uniform magnetic field, the energy spectrum and also the solutions of the Dirac equation are changed in 3+1 dimensions. In addition, our analysis shows that in 2+1 dimensions, the resulted NC field makes electrons in the zero Landau level rotate not only via a cyclotron motion, but also through the ZBW motion with a frequency proportional to the field which doubles the amplitude of the rotation. In fact, this is a hallmark of the ZBW in graphene that provides a promising way to be tested experimentally.

Graphene has brought forward a lot of new physics. One of them is the emergence of massless Dirac fermions in addition to the electrons and these features are new to physics. In this theoretical study, the signatures for quantum scar and the breakdown of universality in graphene are investigated with reference to the presence of these two types of fermions. Taking the graphene quantum dot (QD) potential as the confining potential, the radial part of Dirac equations are solved numerically. Concentrations of the two component eigen-wavefunctions about classical periodic orbits emerge as the signatures for the quantum scar. The sudden variations, in the ratio of the radial wave-functions (large and small components), R(g/f), with mass ratio $\kappa$ are the signatures for breakdown of universality in graphene. The breakdown of universality occurs for the states k = −1 and k = 1, and the state k = −1 is more susceptible to the breakdown of universality.

A treatment of the trembling motion or Zitterbewegung (ZB) phenomena in the armchair graphene nanoribbons (AGNRs) by using long-wave approximation is presented theoretically. We are first interested to study the time dependence of the average values for the current density in AGNR. The longitudinal and transversal components of the current density operator are derived analytically in the Heisenberg representation. The wave packet in a Gaussian distribution is considered with half-width d and a carrier wave vector in the longitudinal orientation k${}_{xo}$. The average values of the current density which represent the current induced by the motion of the electrons along the nanoribbon are calculated numerically. The interference between two energy branches, or the corresponding upper and lower energy states, leads to the trembling motion in the armchair graphene nanoribbon, and hence, our results emphasized that the phenomena of ZB has an aperiodic and nontransient oscillation in the longitudinal and transversal direction, respectively. The average values for the current density for AGNRs are calculated with extremely large value of N and compared with infinite pristine graphene.

We study the Zitterbewegung effect (trembling motion) in thin films of topological insulators with a hexagonal lattice in the presence of terahertz pulse pumping. We derive the analytical expression for the current density, which describes the current induced by the motion of a wave packet of electrons. The electronic subsystem is considered in the long-wavelength approximation, and the electromagnetic field is treated classically in the approximation of a constant pumping. We reveal the possibility to control individual electron wave packets by manipulating with optical pulses.

We theoretically study Zitterbewegung behavior of electrons in graphene system when the external perpendicular magnetic field exists. The initial state is assumed as a wave packet shape which is the superposition of the positive and negative LLs. The evolution of the dipole moments and the excited electric fields are calculated for the localized and extended wave packets which exhibit different behavior. We further analyze their Fourier spectrum and study which factors affect the excited electric field as it can be directly detected in experiment. The results are analyzed and discussed.

We describe a new phenomenon of zitterbewegung of a free Dirac particle in cosmological spacetimes. Unlike the similar effect theorized by Schrödinger in 1930, the cosmological zitterbewegung is a real, physically attainable effect, which originates from the mixing of positive and negative frequency modes of a field operator in cosmological spacetimes. We briefly discuss the potential for observing this effect in laboratory experiments with trapped ions.

In this paper, we argue in the context of recent advances in Dark Energy that the background Zero Point Field, induces an oscillatory motion which we identify with zitterbewegung. We deduce that this is the origin of inertial mass.

We have studied the Zitterbewegung effect on an infinite two-dimensional sheet with honeycomb lattice. By tuning the perpendicular electric field and the magnetization of the sheet, it can enter different topological phases. We have shown that the phase and magnitude of Zitterbewegung effect, i.e., the jittering motion of electron wavepackets, correlates with the various topological phases. The topological phase diagram can be reconstructed by analyzing these features. Our findings are applicable to materials like silicene, germanene, stanene, etc.

We describe recent research on Zitterbewegung (ZB, trembling motion) of electrons in semiconductors. A brief history of the subject is presented. Zitterbewegung of charge carriers in monolayer and bilayer graphene is elaborated in some detail. Effects of an external magnetic field on ZB are described using monolayer graphene as an example. Nature of electron ZB in crystalline solids is explained. It is proposed to trigger the coherent trembling motion of many electrons by exciting them from the valence to the conduction band by laser pulses and detecting the resulting ZB by nonlinear optical effects. Simulations of the trembling motion in vacuum and in semiconductors are reviewed. A recent experimental observation of the trembling motion in semiconducting material InGaAs is mentioned.

A photon is modeled by an uncharged transluminal energy quantum (TEQ) moving at c sqrt(2) along an open 45-degree helical trajectory with radius R=Lambda/2pi, (where Lambda is the helical pitch or wavelength of the photon). A transluminal spatial model of an electron is composed of a charged pointlike transluminal energy quantum circulating at an extremely high frequency of 2.5 x 10²⁰ hz in a closed, double-looped helical trajectory whose helical pitch or wavelength is one Compton wavelength h/mc. The transluminal energy quantum has energy and momentum but not rest mass, so its speed is not limited by c. The TEQ’s speed is superluminal 57% of the time and subluminal 43% of the time, passing through c twice in each trajectory cycle. The TEQ’s maximum speed in the electron’s rest frame is 2.516 c and its minimum speed is c/sqrt(2), or .707 c . The electron model’s helical trajectory parameters are selected to produce the electron’s spin hbar/2 and approximate (without small QED corrections) magnetic moment ehbar/2m (the Bohr magneton) as well as its Dirac equation-related “jittery motion” (zitterbewegung) angular frequency 2mc²/hbar, amplitude hbar/2mc and internal speed c. The two possible helicities of the electron model correspond to the electron and the positron. With these models, an electron is like a closed circulating photon. The electron’s inertia is proposed to be related to the electron model’s circulating internal momentum mc.

Space is the only quantity which can be directly observed. Its main characteristics, in its 3-dimensional Euclidean form, are describable by a Clifford algebra. There have been attempts to construct physics on the basis of this parameter alone, involving extensions to extra dimensions and non-Euclidean forms of geometry. However, it seems that adding a second Clifford algebra, identical in structure to the first, but commutative to it, and dual to it in that it contains no extra physical information, with the duality determined by a zero totality condition, gives us the mathematical construction that we need for both quantum mechanics and other forms of physics. The results can be explored from many angles, for example, Clifford algebra, group theory, geometry and topology, to produce significant results in fundamental physics.