On the Localization Properties of Weyl Particles

Abstract

In this work, it is shown that Weyl particles can exist at different states in zero electromagnetic field, either as free particles or at localized states. In addition, it is shown that the localization, as well as the energy, of the particles can be fully controlled using simple electric fields, which can easily be realized in practice. These results are particularly important regarding possible practical applications of Weyl particles, both considering solid-state physics in materials supporting these particles and laser physics using ions trapped by laser beams, which can simulate the behavior of Weyl particles.

Degenerate solutions to the Dirac equation for massive particles and their applications in quantum tunneling

“…Furthermore, in [1] we have shown that all solutions to the Weyl equation are degenerate, corresponding to an infinite number of electromagnetic 4potentials, explicitly calculated in Theorem 3.1 in [1]. Some very interesting properties of Weyl particles, mainly regarding their control and localization, are discussed in [2,3].…”

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

“…For designing this device, we rely on the theory developed in a previous work of our group [11], where we have shown that it is possible to fully control the localization of Weyl particles applying an electric field perpendicular to their direction of motion. In more detail, the radius of the region where the Weyl particle is confined is given by the formula [11] ( )…”

“…This device is expected to offer significant advantages over similar devices based on conventional electronics, as exceptionally low response time, increased power efficiency, extremely high bandwidth, etc. Furthermore, due to the remarkable property of Weyl particles to be able to exist in the same quantum state in a wide variety of electromagnetic fields [11,12], we anticipate that the proposed device will offer enhanced robustness against electromagnetic perturbations, providing the opportunity to be used efficiently even in environments with high level of electromagnetic noise. Therefore, WPS is expected to play an important role in the emerging field of Weyltronics [4][5][6][7][8][9][10] and find significant applications in several fields, as telecommunications, signal processing, classical and quantum computing, etc.…”

A General Method for Obtaining Degenerate Solutions to the Dirac and Weyl Equations and a Discussion on the Experimental Detection of Degenerate States

“…In the latter case, the corresponding electromagnetic 4‐potentials are calculated using Theorem 3.1. [ 1 ] In recent articles [ 2–5 ] we have extended these results providing several classes of degenerate solutions to the Dirac and Weyl equations for massive [ 2,5 ] and massless [ 3,4 ] particles, and describing their physical properties and potential applications. Furthermore, we discuss some very interesting properties of Weyl particles, mainly regarding their localization.…”

“…Furthermore, we discuss some very interesting properties of Weyl particles, mainly regarding their localization. [ 4 ] Here, it should be noted that in the present work, as well as in all the aforementioned articles, [ 1–5 ] we use the term degenerate not in its conventional sense, but in a novel way, first introduced by Kechriniotis et al., [ 1 ] describing quantum states which are invariant under a wide variety of electromagnetic fields.…”