Degenerate solutions to the massless Dirac and Weyl equations and a proposed method for controlling the quantum state of Weyl particles

• URL: http://arxiv.org/abs/2010.09846v6
• Date: Tue, 24 May 2022 06:54:49 GMT
• Title: Degenerate solutions to the massless Dirac and Weyl equations and a proposed method for controlling the quantum state of Weyl particles
• Authors: Georgios N. Tsigaridas, Aristides I. Kechriniotis, Christos A. Tsonos and Konstantinos K. Delibasis
• Abstract summary: We show that all solutions to the Weyl equation and a special class of solutions to the Dirac equation are degenerate. A method for fully controlling the quantum state of Weyl particles using appropriate electromagnetic fields is proposed.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In a recent work, we have shown that all solutions to the Weyl equation and a special class of solutions to the Dirac equation are degenerate in the sense that they remain unaltered under the influence of a wide variety of different electromagnetic fields. In this study, our previous work is significantly extended, providing a wide class of degenerate solutions to the Dirac equation for massless particles. The electromagnetic fields corresponding to these solutions are calculated and examples regarding both spatially constant electromagnetic fields and electromagnetic waves are also provided. Furthermore, some general solutions to the Weyl equation are presented, and the corresponding electromagnetic fields are calculated. Based on these results, a method for fully controlling the quantum state of Weyl particles using appropriate electromagnetic fields is proposed. Finally, the transition from degenerate to non-degenerate solutions as the particles acquire mass is discussed.

Related papers

• Generalized Gouy Rotation of Electron Vortex beams in uniform magnetic fields [54.010858975226945]
  We study the dynamics of EVBs in magnetic fields using exact solutions of the relativistic paraxial equation in magnetic fields. We provide a unified description of different regimes under generalized Gouy rotation, linking the Gouy phase to EVB rotation angles. This work offers new insights into the dynamics of EVBs in magnetic fields and suggests practical applications in beam manipulation and beam optics of vortex particles.
  arXiv  Detail & Related papers  (2024-07-03T03:29:56Z)
• Quantum electrodynamics of lossy magnetodielectric samples in vacuum: modified Langevin noise formalism [55.2480439325792]
  We analytically derive the modified Langevin noise formalism from the established canonical quantization of the electromagnetic field in macroscopic media. We prove that each of the two field parts can be expressed in term of particular bosonic operators, which in turn diagonalize the electromagnetic Hamiltonian.
  arXiv  Detail & Related papers  (2024-04-07T14:37:04Z)
• An algorithm for exact analytical solutions for tilted anisotropic Dirac materials [0.0]
  We obtain the exact solutions for bound states of tilted anisotropic Dirac materials under the action of external electric and magnetic fields with translational symmetry. In order to solve the eigenvalue equation that arises from the effective Hamiltonian of these materials, we describe an algorithm that allow us to decouple the differential equations that are obtained for the spinor components.
  arXiv  Detail & Related papers  (2023-04-27T21:09:00Z)
• Helical beams of electrons in a magnetic field: New analytic solutions of the Schr\"odinger and Dirac equations [0.0]
  We derive new solutions of the Schr"odinger, Klein-Gordon and Dirac equations. Our solutions exhibit the behavior of quantum particles which very closely resembles classical helical trajectories.
  arXiv  Detail & Related papers  (2023-03-26T19:09:12Z)
• A general method for obtaining degenerate solutions to the Dirac and Weyl equations and a discussion on the experimental detection of degenerate states [0.0]
  We describe a general method for obtaining degenerate solutions to the Dirac equation, corresponding to an infinite number of electromagnetic 4-potentials and fields. An interesting characteristic of these solutions is that, in the case of Dirac particles with non-zero mass, the degenerate spinors should be localized, both in space and time. Our method is also extended to the cases of massless Dirac and Weyl particles, where the localization of the spinors is no longer required.
  arXiv  Detail & Related papers  (2022-10-05T03:29:19Z)
• Exact quantum-mechanical equations for particle beams [91.3755431537592]
  These equations present the exact generalizations of the well-known paraxial equations in optics. Some basic properties of exact wave eigenfunctions of particle beams have been determined.
  arXiv  Detail & Related papers  (2022-06-29T20:39:36Z)
• Stochastic Variational Approach to Small Atoms and Molecules Coupled to Quantum Field Modes [55.41644538483948]
  We present a variational calculation (SVM) of energies and wave functions of few particle systems coupled to quantum fields in cavity QED. Examples for a two-dimensional trion and confined electrons as well as for the He atom and the Hydrogen molecule are presented.
  arXiv  Detail & Related papers  (2021-08-25T13:40:42Z)
• Molecular Interactions Induced by a Static Electric Field in Quantum Mechanics and Quantum Electrodynamics [68.98428372162448]
  We study the interaction between two neutral atoms or molecules subject to a uniform static electric field. Our focus is to understand the interplay between leading contributions to field-induced electrostatics/polarization and dispersion interactions.
  arXiv  Detail & Related papers  (2021-03-30T14:45:30Z)
• Construction of Dirac spinors for electron vortex beams in background electromagnetic fields [0.0]
  Exact solutions of the Dirac equation, a system of four partial differential equations, are rare. Given the growing number of applications of high energy electron beams interacting with a variety of quantum systems in laser fields, novel methods for finding exact solutions to the Dirac equation are called for. We present a method for building up solutions to the Dirac equation employing a recently introduced approach for the description of spinorial fields and their driving electromagnetic fields in terms of geometric algebras.
  arXiv  Detail & Related papers  (2020-11-25T11:55:37Z)
• Degenerate solutions to the Dirac equation for massive particles and their applications in quantum tunneling [0.0]
  We prove the existence of degenerate solutions to the Dirac equation, corresponding to an infinite number of different electromagnetic fields. We calculate the electromagnetic fields corresponding to these solutions, providing some examples regarding both spatially constant electromagnetic fields and electromagnetic waves.
  arXiv  Detail & Related papers  (2020-10-19T20:34:33Z)
• General quantum-mechanical solution for twisted electrons in a uniform magnetic field [68.8204255655161]
  A theory of twisted (and other structured) paraxial electrons in a uniform magnetic field is developed. The observable effect of a different behavior of relativistic Laguerre-Gauss beams with opposite directions of the orbital angular momentum penetrating from the free space into a magnetic field is predicted.
  arXiv  Detail & Related papers  (2020-05-13T16:35:10Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.