9 research outputs found
Asymmetric Wave Propagation Through Nonlinear PT-symmetric Oligomers
In the present paper, we consider nonlinear PT-symmetric dimers and trimers
(more generally, oligomers) embedded within a linear Schr{\"o}dinger lattice.
We examine the stationary states of such chains in the form of plane waves, and
analytically compute their reflection and transmission coefficients through the
nonlinear PT symmetric oligomer, as well as the corresponding rectification
factors which clearly illustrate the asymmetry between left and right
propagation in such systems. We examine not only the existence but also the
dynamical stability of the plane wave states and interestingly find them to be
generically unstable. Lastly, we generalize our numerical considerations to the
more physically relevant case of Gaussian initial wavepackets and confirm that
the asymmetry in the transmission properties persists in the case of such
wavepackets, as well
Scalar field exact solutions for non-flat FLRW cosmology: A technique from non-linear Schr\"odinger-type formulation
We report a method of solving for canonical scalar field exact solution in a
non-flat FLRW universe with barotropic fluid using non-linear Schr\"{o}dinger
(NLS)-type formulation in comparison to the method in the standard Friedmann
framework. We consider phantom and non-phantom scalar field cases with
exponential and power-law accelerating expansion. Analysis on effective
equation of state to both cases of expansion is also performed. We speculate
and comment on some advantage and disadvantage of using the NLS formulation in
solving for the exact solution.Comment: 12 pages, GERG format, Reference added. accepted by Gen. Relativ. and
Gra
Slow-roll, acceleration, the Big Rip and WKB approximation in NLS-type formulation of scalar field cosmology
Aspects of non-linear Schr\"{o}dinger-type (NLS) formulation of scalar
(phantom) field cosmology on slow-roll, acceleration, WKB approximation and Big
Rip singularity are presented. Slow-roll parameters for the curvature and
barotropic density terms are introduced. We reexpress all slow-roll parameters,
slow-roll conditions and acceleration condition in NLS form. WKB approximation
in the NLS formulation is also discussed when simplifying to linear case. Most
of the Schr\"{o}dinger potentials in NLS formulation are very slowly-varying,
hence WKB approximation is valid in the ranges. In the NLS form of Big Rip
singularity, two quantities are infinity in stead of three. We also found that
approaching the Big Rip, , which is the
same as effective phantom equation of state in the flat case.Comment: [7 pages, no figure, more reference added, accepted by JCAP
Dynamics of generalized PT-symmetric dimers with time-periodic gainâloss
A parity-time (PT)-symmetric system with periodically varying-in-time gain and loss modeled by two coupled Schrödinger equations (dimer) is studied. It is shown that the problem can be reduced to a perturbed pendulum-like equation. This is done by finding two constants of motion. Firstly, a generalized problem using Melnikov-type analysis and topological degree arguments is studied for showing the existence of periodic (libration), shift- periodic (rotation), and chaotic solutions. Then these general results are applied to the PT-symmetric dimer. It is interestingly shown that if a sufficient condition is satisfied, then rotation modes, which do not exist in the dimer with constant gainâloss, will persist. An approximate threshold for PT-broken phase corresponding to the disappearance of bounded solutions is also presented. Numerical study is presented accompanying the analytical results