19 research outputs found
Exotic Phase Space Dynamics Generated by Orthogonal Polynomial Self-interactions
The phase space dynamics generated by different orthogonal polynomial
self-interactions exhibited in higher order nonlinear Schr\"{o}dinger equation
(NLSE) are often less intuitive than those ofcubic and quintic nonlinearities.
Even for nonlinearities as simple as a cubic in NLSE, the dynamics for generic
initial states shows surprising features. In this Letter, for the first time,
we identify the higher-order nonlinearities in terms of orthogonal polynomials
in the generalized NLSE/GPE. More pertinently, we explicate different exotic
phase space structures for three specific examples: (i) Hermite, (ii)
Chebyshev, and (iii) Laguerre polynomial self-interactions. For the first two
self-interactions, we exhibit that the alternating signs of the various
higher-order nonlinearities are naturally embedded in these orthogonal
polynomials that confirm to the experimental conditions. To simulate the
phase-space dynamics that bring about by the Laguerre self-interactions, a
source term should {\it necessarily} be included in the modified NLSE/GPE.
Recent experiments suggest that this modified GPE captures the dynamics of
self-bound quantum droplets, in the presence of external source
Time dependent non-Abelian waves and their stochastic regimes for gauge fields coupled to external sources
In this paper we explore explicit exact solutions of the Yang-Mills
(YM) and Yang-Mill-Higgs (YMH) equations with homogeneous and inhomogeneous
external sources. Whereas in the case of YM we have confirmed our analytical
findings with the numerical simulations, the numerical corroborations in the
YMH case yielded the stochastic character of motion for the ensuing fields.Comment: 6 pages 16 Figure
Classical solutions for Yang-Mills-Chern-Simons field coupled to an external source
We find wide class of exact solutions of Yang-Mills-Chern-Simons theory
coupled to an external source, in terms of doubly periodic Jacobi elliptic
functions. The obtained solutions include localized solitons, trigonometric
solutions, pure cnoidal waves, and singular solutions in certain parameter
range. Furthermore, it is observed that these solutions exist over a nonzero
background.Comment: 5 page
Sinusoidal Excitations in Two Component Bose-Einstein Condensates
The non-linear coupled Gross-Pitaevskii equation governing the dynamics of
the two component Bose-Einstein condensate (TBEC) is shown to admit pure
sinusoidal, propagating wave solutions in quasi one dimensional geometry. These
solutions, which exist for a wide parameter range, are then investigated in the
presence of a harmonic oscillator trap with time dependent scattering length.
This illustrates the procedure for coherent control of these modes through
temporal modulation of the parameters, like scattering length and oscillator
frequency. We subsequently analyzed this system in an optical lattice, where
the occurrence of an irreversible phase transition from superfluid to insulator
phase is seen.Comment: 6 pages, 1 figur