Different electromagnetic physical representations of the Dirac's oscillator according with its spatial dimension

• URL: http://arxiv.org/abs/2005.09061v2
• Date: Fri, 19 Jun 2020 05:13:52 GMT
• Title: Different electromagnetic physical representations of the Dirac's oscillator according with its spatial dimension
• Authors: Juan Sebasti\'an Monta\~nez Moyano (1), Carlos Jos\'e Quimbay Herrera (1) ((1) Universidad Nacional de Colombia)
• Abstract summary: Dirac's oscillator (DO) is one of the most studied systems in the Relativistic Quantum Mechanics. In (3+1)dimensions the DO represents a relativistic and electrically neutral fermion with magnetic dipole momentum. In (1+1) dimensions DO reproduces a relativistic and electrically charged fermion interacting with a linear electric field.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Dirac's oscillator (DO) is one of the most studied systems in the Relativistic Quantum Mechanics and in the physical-mathematics. In particular, we show that this system has an unique property which it has not ever seen in other known systems: According to its spatial dimensionality, DO represent physical systems with very different electromagnetic nature. So far in the literature, it has been proved using the covariant method the gauge invariance of the Dirac's oscillator potential. It has also shown that in (3+1)dimensions the DO represents a relativistic and electrically neutral fermion with magnetic dipole momentum, into a dielectric medium with spherical symmetry and under the effect of an electric field which depends of the radial distance. In this work,and using the same methodology, we show that (2+1) dimensional DO represents a 1/2-spin relativistic fermion under the effect of a uniform and perpendicular external magnetic field; whereas in (1+1) dimensions DO reproduces a relativistic and electrically charged fermion interacting with a linear electric field. Additionally, we prove that DO does not have chiral invariance, independent of its dimensionality, due to the interaction potential which breaks explicitly the chiral symmetry $U(1)_R \times U(1)_L$ but it preserves the global gauge symmetry $U(1)$.

Related papers

• Symmetry generators and quantum numbers for fermionic circularly symmetric motion [0.0]
  We derive the generators for the continuous symmetries of the 3+1 Dirac equation for planar motion. We also derive the generators of the spin and pseudospin symmetries for this planar Dirac problem.
  arXiv  Detail & Related papers  (2024-09-10T20:18:55Z)
• Unveiling the Quantum Toroidal Dipole in Nanosystems: Quantization, Interaction Energy, and Measurement [44.99833362998488]
  We investigate a quantum particle confined to a toroidal surface in the presence of a filiform current along the system's rotational axis. Our analysis reveals that the interaction between the particle and the current induces a non-zero toroidal dipole in the particle's stationary states.
  arXiv  Detail & Related papers  (2024-01-26T13:31:32Z)
• Two-dimensional lattice with an imaginary magnetic field [0.0]
  We introduce a two-dimensional non-Hermitian lattice model with an imaginary magnetic field. We show that the energy spectrum does not converge as lattice size is made larger, which comes from the intrinsic nonperiodicity of the model. We also find an analog of the Aharonov-Bohm effect; the net change of the norm of the wave function upon adiabatically forming a closed path is determined by the imaginary magnetic flux enclosed by the path.
  arXiv  Detail & Related papers  (2023-07-27T05:50:24Z)
• Dirac materials in parallel non-uniform electromagnetic fields generated by SUSY: A new class of chiral Planar Hall Effect? [0.0]
  We find a nontrivial current density in the same plane where the electric and magnetic fields lie, but perpendicular to both of them. This density is the sum of current densities for the left- and right-chiralities, suggesting that the net current is a consequence of chiral symmetry.
  arXiv  Detail & Related papers  (2023-06-28T17:48:56Z)
• Foldy-Wouthuysen transformation and multiwave states of a graphene electron in external fields and free (2+1)-space [91.3755431537592]
  Graphene electrons in a static electric field can exist in the multiwave Hermite-Gauss states defining non-spreading coherent beams. It is proven that the Hermite-Gauss beams exist even in the free space.
  arXiv  Detail & Related papers  (2023-05-07T17:03:00Z)
• Topology, nonlocality and duality in classical electrodynamics [0.0]
  We argue that classical electrodynamics can predict nonlocal effects by showing an example of a topological and nonlocal electromagnetic angular momentum. We unify both angular momenta by means of the electromagnetic angular momentum arising in the configuration formed by a dyon encircling an infinitely-long dual solenoid. We verify that this duality-invariant electromagnetic angular momentum is insensitive to the radiative effects of the Li'enard-Wiechert fields of the encircling dyon.
  arXiv  Detail & Related papers  (2022-04-26T20:43:27Z)
• Fast electrons interacting with chiral matter: mirror symmetry breaking of quantum decoherence and lateral momentum transfer [91.3755431537592]
  We show that matter chirality breaks mirror symmetry of scattered electrons quantum decoherence. We also prove that mirror asymmetry also shows up in the distribution of the electron lateral momentum.
  arXiv  Detail & Related papers  (2022-04-07T15:06:27Z)
• Dispersive readout of molecular spin qudits [68.8204255655161]
  We study the physics of a magnetic molecule described by a "giant" spin with multiple $d > 2$ spin states. We derive an expression for the output modes in the dispersive regime of operation. We find that the measurement of the cavity transmission allows to uniquely determine the spin state of the qudits.
  arXiv  Detail & Related papers  (2021-09-29T18:00:09Z)
• Duality Symmetry of Quantum Electrodynamics and Magnetic Charges [8.19841678851784]
  duality symmetry between electricity and magnetism hidden in classical Maxwell equations. In quantum electrodynamics (QED), both the electric and magnetic fields have been unified into one gauge field. We show that the electric-magnetic duality symmetry cannot give any new conservation law.
  arXiv  Detail & Related papers  (2021-03-01T13:46:45Z)
• Collective spontaneous emission of two entangled atoms near an oscillating mirror [50.591267188664666]
  We consider the cooperative spontaneous emission of a system of two identical atoms, interacting with the electromagnetic field in the vacuum state. Using time-dependent theory, we investigate the spectrum of the radiation emitted by the two-atom system. We show that it is modulated in time, and that the presence of the oscillating mirror can enhance or inhibit the decay rate.
  arXiv  Detail & Related papers  (2020-10-07T06:48:20Z)
• 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.