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

Tsigaridas, G.; Kechriniotis, Aristides I.; Tsonos, Christos A.; Delibasis, Konstantinos K.

doi:10.1016/j.cjph.2022.04.010

Cited by 5 publications

(9 citation statements)

References 19 publications

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“…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].…”

Section:      =+mentioning

confidence: 90%

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

et al. 2021

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In a recent work we have proven the existence of degenerate solutions to the Dirac equation, corresponding to an infinite number of different electromagnetic fields, providing also some examples regarding massless particles. In the present article our results are extended significantly, providing degenerate solutions to the Dirac equation for particles with arbitrary mass, which, under certain conditions, could be interpreted as pairs of particles (or antiparticles) moving in a potential barrier with energy equal to the height of the barrier and spin opposite to each other. We calculate the electromagnetic fields corresponding to these solutions, providing also some examples regarding both spatially constant electromagnetic fields and electromagnetic waves. Further, we discuss some potential applications of our work, mainly regarding the control of the particles outside the potential barrier, without affecting their state inside the barrier. Finally, we study the effect of small perturbations to the degenerate solutions, showing that our results are still valid, in an approximate sense, provided that the amplitude of the electromagnetic fields corresponding to the exact degenerate solutions is sufficiently small.

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Section:      =+mentioning

confidence: 90%

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

et al. 2021

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“…[10][11][12][13][14][15] Furthermore, the state of Weyl and massless Dirac particles described by degenerate spinors, will not be affected by the presence of a plane electromagnetic wave, e.g., a laser beam of arbitrary polarization, propagating along the direction of motion of the particles. [3] Thus, particles in degenerate states, as well as electromagnetic waves can propagate along the same direction without interacting with each other, which obviously is not the case for charged particles in nondegenerate states.…”

Section: On the Experimental Detection Of Degenerate Statesmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2023

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In this work, a general method is described for obtaining degenerate solutions of the Dirac equation, corresponding to an infinite number of electromagnetic 4-potentials and fields, which are explicitly calculated. More specifically, using four arbitrary real functions, one can automatically construct a spinor that satisfies the Dirac equation for an infinite number of electromagnetic 4-potentials, defined by those functions. An interesting characteristic of these solutions is that, in the case of Dirac particles with nonzero mass, the degenerate spinors should be localized, both in space and time. The method is also extended to the cases of massless Dirac and Weyl particles, where the localization of the spinors is no longer required. Finally, two experimental methods are proposed for detecting the presence of degenerate states.

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“…In a recent work, [ 2 ] we have shown that all spinors of the form

\begin{equation}\hspace*{8pc}\psi = \left( { \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} {\cos \left( {\frac{{\theta \left( t \right)}}{2}} \right)}\\ {{{\rm{e}}^{{\rm{i}}\varphi \left( t \right)}}\sin \left( {\frac{{\theta \left( t \right)}}{2}} \right)} \end{array} } \right){\rm{exp}}\left[ {{\rm{i}}h\left( {{\bf{r}},t} \right)} \right]\end{equation}

…”

Section: Introductionmentioning

confidence: 99%

On the Localization Properties of Weyl Particles

et al. 2022

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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.

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

Cited by 5 publications

References 19 publications

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

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

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

On the Localization Properties of Weyl Particles

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