A field-theoretical space-time position operator can be properly introduced for the Dirac field, it plays the role of a generalized Noether charge associated with a local symmetry, and its second-quantized form shows that quantum fields possess zero-point time, which implies that a zero-point fluctuation of energy must be accompanied with a zero-point fluctuation of time, and then in agreement with the time-energy uncertainty principle. In practice, some possible physical effects owing to zero-point time remain to be found.
Comment on "Position-dependent effective mass Dirac equations with PT- symmetric and non - PT- symmetric potentials" [J. Phys. A: Math. Gen. 39 (2006) 11877--11887]
It is shown that the paper `Energy spectrum of a Dirac particle with position-dependent mass under the influence of the Aharonov-Casher effect', by Oliveira, Borges and Sousa [Braz. J. Phys. 49, 801 (2019)], is based on a series of ingredients clearly incorrect.
We construct a Darboux transformation for a class of two-dimensional Dirac systems at zero energy. Our starting equation features a position-dependent mass, a matrix potential, and an additional degree of freedom that can be interpreted either as a magnetic field perpendicular to the plane or a generalized Dirac oscillator interaction. We obtain a number of Darbouxtransformed Dirac equations for which the zero energy solutions are exactly known.
We solve the one-dimensional Dirac equation by taking into account the possibility of position-dependence in the mass function. We also take the Fermi velocity to act as a local variable and examine the combined effects of the two on the solvability of the Dirac equation with respect to the Morse potential. Our results for the wave functions and the energy levels corresponding to such an extended scheme are furnished in closed forms.
We investigate the (1+1)-dimensional position-dependent mass Dirac equation within the confines of so(2,1) potential algebra by utilizing the character of a spatial varying Fermi velocity. We examine the combined effects of the two when the Dirac equation is equipped with an external pseuodoscalar potential. Solutions of the three cases induced by so(2, 1) are explored by profitably making use of a point canonical transformation.
We present a new approach to study (1+1)-dimensional Dirac equation in the background of an effective mass $M$ by exploiting the possibility of a position-dependent fermi velocity $v_f$. We explore the resulting structure of the coupled equations and arrive at an interesting constraint of $M$ turning out to be the inverse square of $v_f$. We address several solutions of the effective potential that include the free particle, shifted harmonic oscillator, Morse potential, and CPRS potential.
We study the $(1+1)$ dimensional generalized Dirac oscillator with a position-dependent mass. In particular, bound states with zero energy as well as non zero energy have been obtained for suitable choices of the mass function/oscillator interaction. It has also been shown that in the presence of an electric field, bound states exist if the magnitude of the electric field does not exceed a critical value.
Spectral analysis of Dirac materials in position-dependent magnetic and electric fields via Heun functions
Escuela Superior de Física y Matemáticas del Instituto Politécnico Nacional（墨西哥国立理工学院物理与数学高等学院）；Área Académica de Matemáticas y Física, UAEH（伊达尔戈自治大学数学与物理学术区）
Dependency on the preparation of state for the Heisenberg uncertainty principle can be removed with the help of entropy uncertainty principle. The shortness of the uncertainty principle (UP) can be overcome with the help of the concept of Shannon's information entropy (SE). In this article, we have shown that UP in terms of SE holds for a position-dependent effective mass system. We have considered the Dirac system with a mass-jump at the origin. We have proved the existence of a lower bound for a UP for this position-dependent effective mass.
In every state of a quantum particle, Wigner's quasidistribution is the unique quasidistribution on the phase space with the correct marginal distributions for position, momentum, and all their linear combinations.
Reporting about the Wigner formalism for describing Dirac spinor structures through a covariant phase-space formulation, the quantum information quantifiers for purity and mutual information involving spin-parity (discrete) and position-momentum (continuous) degrees of freedom are consistently obtained. For Dirac spinor Wigner operators decomposed into Poincaré classes of $SU(2) \otimes SU(2)$ spinor couplings, a definitive expression for quantum purity is identified in a twofold way: firstly, in terms of phase-space positively defined quantities, and secondly, in terms of the {\em spin-parity…
The Dirac equation in $(2+1)$ dimensions on the toroidal surface is studied for a massless fermion particle under the action of external fields. Using the covariant approach based on general relativity, the Dirac operator stemming from a metric related to the strain tensor is discussed within the Pseudo-Hermitian operator theory. Furthermore, analytical solutions are obtained for two cases, namely, constant and position-dependent Fermi velocity.
It is shown that the carrier of a bounded localized free Dirac wavefunction shrinks from infinity and subsequently expands to infinity again. The motion occurs isotropicly at the speed of light. In between there is the phase of rebound, which is limited in time and space in the order of the diameter of the carrier at its minimal extension. This motion proceeds anisotropicly and abruptly as for every direction in space there is a specific time, at which the change from shrinking to expanding happens instantaneously. Asymptotically, regarding the past and the future as well, the probability of p…
