Delay time computation for relativistic tunneling particles

Bernardini, Alex E.

doi:10.1140/epjc/s10052-008-0571-0

Cited by 6 publications

(4 citation statements)

References 51 publications

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“…Our approach is three dimensional but the assumed stratified direction (x axis) of the potential together with the incoming three momentum determines the scattering plane within which lie both the reflected and transmitted momenta. We shall call this the x-y plane and hence, without lose of generality, we consider planar scattering, both diffusion and tunnelling [2][3][4][5][6][7][8][9][10][11][12][13][14]. Our spinors are Dirac spinors.…”

Section: Introductionmentioning

confidence: 99%

Relative helicity phases in planar Dirac scattering

Rotelli

2012

Phys. Rev. A

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Section: Introductionmentioning

confidence: 99%

Relative helicity phases in planar Dirac scattering

Rotelli

2012

Phys. Rev. A

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“…In section VI we compute the tunneling transmission probabilities and the respective delay-times for wave packets when a relativistic dynamic is taken into account [17,18]. The transmission probabilities, the phase times and the dwell times for the relativistic dynamics are all obtained and the conditions for the occurrence of accelerated and, eventually, superluminal tunneling transmission probabilities are specified.…”

Section: Introductionmentioning

confidence: 99%

Stationary phase method and delay times for relativistic and non-relativistic tunneling particles

Bernardini

2009

Annals of Physics

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This report deals with the basic concepts on deducing transit times for quantum scattering: the stationary phase method and its relation with delay times for relativistic and non-relativistic tunneling particles. After reexamining the above-barrier diffusion problem, we notice that the applicability of this method is constrained by several subtleties in deriving the phase time that describes the localization of scattered wave packets. Using a recently developed procedure -multiple wave packet decomposition -for some specifical colliding configurations, we demonstrate that the analytical difficulties arising when the stationary phase method is applied for obtaining phase (traversal) times are all overcome. In this case, we also investigate the general relation between phase times and dwell times for quantum tunneling/scattering. Considering a symmetrical collision of two identical wave packets with an one-dimensional barrier, we demonstrate that these two distinct transit time definitions are explicitly connected. The traversal times are obtained for a symmetrized (two identical bosons) and an antisymmetrized (two identical fermions) quantum colliding configuration. Multiple wave packet decomposition shows us that the phase time (group delay) describes the exact position of the scattered particles and, in addition to the exact relation with the dwell time, leads to correct conceptual understanding of both transit time definitions.At last, we extend the non-relativistic formalism to the solutions for the tunneling zone of a onedimensional electrostatic potential in the relativistic (Dirac to Klein-Gordon) wave equation where the incoming wave packet exhibits the possibility of being almost totally transmitted through the potential barrier. The conditions for the occurrence of accelerated and, eventually, superluminal tunneling transmission probabilities are all quantified and the problematic superluminal interpretation based on the non-relativistic tunneling dynamics is revisited. Lessons concerning the dynamics of relativistic tunneling and the mathematical structure of its solutions suggest revealing insights into mathematically analogous condensed-matter experiments using electrostatic barriers in single-and bi-layer graphene, for which the accelerated tunneling effect deserves a more careful investigation.

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“…Some preliminary issues have already investigated the relativistic linear transmission [14][15][16][17] and the phenomena of planar diffusion of Dirac particles [18][19][20] through and above potential barriers and steps. In particular, the effects of relative phases between incoming and reflected or transmitted amplitude components of diffused waves have been accurately quantified [14,21,22].…”

Section: Introductionmentioning

confidence: 99%

SU(2)⊗SU(2) bi-spinor structure entanglement induced by a step potential barrier scattering in two-dimensions

2015

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Please cite this article as: V.A.S.V. Bittencourt, et al., SU (2) ⊗ SU (2) bi-spinor structure entanglement induced by a step potential barrier scattering in two-dimensions, Annals of Physics (2015), http://dx. AbstractThe entanglement between SU (2) ⊗ SU (2) internal degrees of freedom of parity and helicity for reflected and transmitted waves of Dirac-like particles scattered by a potential step along an arbitrary direction on the x − y plane is quantified. Diffusion (E ≥ V ) and Klein zone (V ≥ E) energy regimes are considered. It has been shown that, for SU (2) ⊗ SU (2) polarized structures of helicity eigenstates impinging the barrier, the local interaction with a step potential destroys the parity-spin separability. The framework presented here can be straightforwardly translated into a useful theoretical tool for obtaining the spin-spin entanglement in the context of enlarged scenarios of nonrelativistic 2D systems, as for instance those for describing single layer graphene, or even single trapped ions with Dirac bi-spinor mathematical structure.

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Delay time computation for relativistic tunneling particles

Cited by 6 publications

References 51 publications

Relative helicity phases in planar Dirac scattering

Relative helicity phases in planar Dirac scattering

Stationary phase method and delay times for relativistic and non-relativistic tunneling particles

SU(2)⊗SU(2) bi-spinor structure entanglement induced by a step potential barrier scattering in two-dimensions

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