Spinor solitons and their PT -symmetric offspring

Alexeeva, N. V.; Barashenkov, I. V.; Saxena, A.

doi:10.1016/j.aop.2018.11.010

Title: Spinor solitons and their $PT$ -symmetric offspring

Journal Article · 16 November 2018 · Annals of Physics

DOI: https://doi.org/10.1016/j.aop.2018.11.010 · OSTI ID:1524390

Alexeeva, N. V. ^[1]; Barashenkov, I. V. ^[1]; Saxena, A. ^[2]

Univ. of Cape Town (South Africa); Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of Bath, Claverton Down, Bath (United Kingdom)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

While the spinor field in (1+1) dimensions has the right structure to model a dispersive bimodal system with gain and loss, the plain addition of gain to one component of the field and loss to the other one results in an unstable dispersion relation. Here, we advocate a different recipe for the $PT$ -symmetric extension of spinor models — the recipe that does not produce instability of the linear Dirac equation. Having exemplified the physical origins of the $P- and T-$ breaking terms, we consider the extensions of three U(1)-invariant spinor models with cubic nonlinearity. Of these, the $PT$ -symmetric extension of the Thirring model is shown to be completely integrable and possess infinitely many conserved quantities. The $PT$ -symmetric Gross–Neveu equation conserves energy and momentum but does not conserve charge. The third model is introduced for the purpose of comparison with the previous two; its $PT$ -symmetric extension has no conservation laws at all. Despite this dramatic difference in the integrability and conservation properties, all three $PT$ -symmetric models are shown to have exact soliton solutions. Similar to the solitons of the extended Thirring and Gross–Neveu equations, the solitons of the new model are found to be stable — except for a narrow band of frequencies adjacent to the soliton existence boundary. The persistence under the $P- and T-$ breaking perturbations as well as the prevalence of stability highlights a remarkable sturdiness of spinor solitons in (1+1) dimensions.

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Research Organization:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: National Research Foundation of South Africa; USDOE

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1524390

Report Number(s):: LA-UR--17-31368

Journal Information:: Annals of Physics, Journal Name: Annals of Physics Journal Issue: C Vol. 403; ISSN 0003-4916

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Title: Spinor solitons and their $PT$ -symmetric offspring