Spinor solitons and their PT-symmetric offspring

Journal Article · Mon Apr 15 04:00:00 EDT 2019 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2018.11.010· OSTI ID:22852373

Although 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. In this paper, 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.

• OSTI ID: 22852373
• Journal Information: Annals of Physics, Journal Name: Annals of Physics Vol. 403; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CONSERVATION LAWS
DIRAC EQUATION
DISPERSION RELATIONS
DISTURBANCES
EXACT SOLUTIONS
INTEGRABILITY
NONLINEAR PROBLEMS
PARITY
PERTURBATION THEORY
SOLITONS
SPINOR FIELDS
SYMMETRY
THIRRING MODEL