Title: Speed-of-light pulses in the massless nonlinear Dirac equation with a potential

Abstract

In this work, we consider the massless nonlinear Dirac (NLD) equation in $1+1$ dimension with scalar-scalar self-interaction $\frac{g^2}{2}{\left(\overline{\mathrm{\Psi }}\mathrm{\Psi }\right)}^2$ in the presence of three external electromagnetic real potentials $V\left(x\right)$, a potential barrier, a constant potential, and a potential well. By solving numerically the NLD equation, we find different scenarios depending on initial conditions, namely, propagation of the initial pulse along one direction, splitting of the initial pulse into two pulses traveling in opposite directions, and focusing of two initial pulses followed by a splitting. For all considered cases, the final waves travel with the speed of light and are solutions of the massless linear Dirac equation. During these processes the charge and the energy are conserved, whereas the momentum is conserved when the solutions possess specific symmetries. For the case of the constant potential, we derive exact analytical solutions of the massless NLD equation that are also solutions of the massless linearized Dirac equation. Decay or growth of the initial pulse is also predicted from the evolution of the charge for the case of a non-zero imaginary part of the potential.

Authors:

Quintero, Niurka R. ^[1]; Mertens, Franz G. ^[2]; Cooper, Fred ^[3]; Saxena, Avadh  ^[4];

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Bishop, Alan R. ^[4]

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+ Show Author Affiliations

1. Escuela Politécnica Superior (EPS), Sevilla (Spain); Univ. de Granada (Spain)
2. Univ. Bayreuth (Germany)
3. Santa Fe Inst. (SFI), Santa Fe, NM (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
4. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:

Wed Nov 22 00:00:00 EST 2017

Research Org.:

Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Org.:

USDOE Laboratory Directed Research and Development (LDRD) Program; Ministerio de Economía y Competitividad (MINECO); Junta de Andalucía

OSTI Identifier:

1688733

Alternate Identifier(s):

OSTI ID: 1409871

Report Number(s):

LA-UR-17-24149
Journal ID: ISSN 2470-0045; TRN: US2204131

Grant/Contract Number:  

89233218CNA000001; FIS2014-54497-P; P11-FQM-7276

Resource Type:

Accepted Manuscript

Journal Name:

Physical Review. E

Additional Journal Information:

Journal Volume: 96; Journal Issue: 5; Journal ID: ISSN 2470-0045

Publisher:

American Physical Society (APS)

Country of Publication:

United States

Language:

English

Subject:

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Mathematics