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Nonlinear Dirac solitons in external fields | | Franz G. Mertens
; Niurka R. Quintero
; Fred Cooper
; Avinash Khare
; Avadh Saxena
; | | Date: |
10 Aug 2012 | | Abstract: | We consider the nonlinear Dirac equations (NLDE’s) in 1+1 dimension with
scalar-scalar self interaction $frac{g^2}{kappa+1} ({Psi} Psi)^{kappa+1}$
in the presence of various external electromagnetic fields. We find exact
solutions for special external fields and we study the behavior of solitary
wave solutions to the NLDE in the presence of a wide variety of fields in a
variational approximation depending on collective coordinates which allows the
position, width and phase of these waves to vary in time. We find that in this
approximation the position $q(t)$ of the center of the solitary wave obeys the
usual behavior of a relativistic point particle in an external field. For time
independent external fields we find that the energy of the solitary wave is
conserved but not the momentum which becomes a function of time. We postulate
that similar to the nonlinear Schr{"o}dinger equation (NLSE) that a sufficient
dynamical condition for instability to arise is that $ dP(t)/d dq(t) < 0$.
Here $P(t)$ is the momentum of the solitary wave, and $dq$ is the velocity of
the center of the wave. We investigate the accuracy of our variational
approximation using numerical simulations of the NLDE and find that when the
forcing term is small and we are in a regime where the solitary wave is stable,
that the behavior of the solutions of the collective coordinate equations
agrees very well with the numerical simulations. | | Source: | arXiv, 1208.2090 | | Services: | Forum | Review | PDF | Favorites | |
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