274 research outputs found
Enhancement of Persistent Currents by Hubbard Interactions In Disordered 1D Rings: Avoided Level Crossings Interpretation
We study effects of local electron interactions on the persistent current of
one dimensional disordered rings. For different realizations of disorder we
compute the current as a function of Aharonov-Bohm flux to zeroth and first
orders in the Hubbard interaction. We find that the persistent current is {\em
enhanced} by onsite interactions. Using an avoided level crossings approach, we
derive analytic formulas which explain the numerical results at weak disorder.
The same approach also explains the opposite effect (suppression) found for
spinless fermion models with intersite interactions.Comment: uuencoded: 17 pages, text in revtex, 7 figs in postscrip
Scattering of gap solitons by PT-symmetric defects
The resonant scattering of gap solitons (GS) of the periodic nonlinear
Schr\"odinger equation with a localized defect which is symmetric under the
parity and the time-reversal (PT) symmetry, is investigated. It is shown that
for suitable amplitudes ratios of the real and imaginary parts of the defect
potential the resonant transmission of the GS through the defect becomes
possible. The resonances occur for potential parameters which allow the
existence of localized defect modes with the same energy and norm of the
incoming GS. Scattering properties of GSs of different band-gaps with effective
masses of opposite sign are investigated. The possibility of unidirectional
transmission and blockage of GSs by PT defect, as well as, amplification and
destruction induced by multiple reflections from two PT defects, are also
discussed
Discrete gap solitons in a diffraction-managed waveguide array
A model including two nonlinear chains with linear and nonlinear couplings
between them, and opposite signs of the discrete diffraction inside the chains,
is introduced. For [] nonlinearity, the model finds two different
interpretations in terms of optical waveguide arrays, based on the
diffraction-management concept. A straightforward discrete []
model, with opposite signs of the diffraction at the fundamental and second
harmonics, is introduced also. Starting from the anti-continuum (AC) limit,
soliton solutions in the model are found, both above the phonon
band and inside the gap. Solitons above the gap may be stable as long as they
exist, but in the transition to the continuum limit they inevitably disappear.
On the contrary, solitons inside the gap persist all the way up to the
continuum limit. In the zero-mismatch case, they lose their stability long
before reaching the continuum limit, but finite mismatch can have a stabilizing
effect on them. A special procedure is developed to find discrete counterparts
of the Bragg-grating gap solitons. It is concluded that they exist all the
values of the coupling constant, but are stable only in the AC and continuum
limits. Solitons are also found in the model. They start as
stable solutions, but then lose their stability. Direct numerical simulations
in the cases of instability reveal a variety of scenarios, including
spontaneous transformation of the solitons into breather-like states,
destruction of one of the components (in favor of the other), and
symmetry-breaking effects. Quasi-periodic, as well as more complex, time
dependences of the soliton amplitudes are also observed as a result of the
instability development.Comment: 18 pages, 27 figures, Eur. Phys. J. D in pres
Stable vortex and dipole vector solitons in a saturable nonlinear medium
We study both analytically and numerically the existence, uniqueness, and
stability of vortex and dipole vector solitons in a saturable nonlinear medium
in (2+1) dimensions. We construct perturbation series expansions for the vortex
and dipole vector solitons near the bifurcation point where the vortex and
dipole components are small. We show that both solutions uniquely bifurcate
from the same bifurcation point. We also prove that both vortex and dipole
vector solitons are linearly stable in the neighborhood of the bifurcation
point. Far from the bifurcation point, the family of vortex solitons becomes
linearly unstable via oscillatory instabilities, while the family of dipole
solitons remains stable in the entire domain of existence. In addition, we show
that an unstable vortex soliton breaks up either into a rotating dipole soliton
or into two rotating fundamental solitons.Comment: To appear in Phys. Rev.
A generalized Petviashvili iteration method for scalar and vector Hamiltonian equations with arbitrary form of nonlinearity
The Petviashvili's iteration method has been known as a rapidly converging
numerical algorithm for obtaining fundamental solitary wave solutions of
stationary scalar nonlinear wave equations with power-law nonlinearity: \
, where is a positive definite self-adjoint operator and . In this paper, we propose a systematic generalization of this method
to both scalar and vector Hamiltonian equations with arbitrary form of
nonlinearity and potential functions. For scalar equations, our generalized
method requires only slightly more computational effort than the original
Petviashvili method.Comment: to appear in J. Comp. Phys.; 35 page
Nonlinear dynamics of wave packets in PT-symmetric optical lattices near the phase transition point
Nonlinear dynamics of wave packets in PT-symmetric optical lattices near the
phase-transition point are analytically studied. A nonlinear Klein-Gordon
equation is derived for the envelope of these wave packets. A variety of novel
phenomena known to exist in this envelope equation are shown to also exist in
the full equation including wave blowup, periodic bound states and solitary
wave solutions.Comment: 4 pages, 2 figure
-Symmetric Periodic Optical Potentials
In quantum theory, any Hamiltonian describing a physical system is mathematically represented by a self-adjoint linear operator to ensure the reality of the associated observables. In an attempt to extend quantum mechanics into the complex domain, it was realized few years ago that certain non-Hermitian parity-time () symmetric Hamiltonians can exhibit an entirely real spectrum. Much of the reported progress has been remained theoretical, and therefore hasn't led to a viable experimental proposal for which non Hermitian quantum effects could be observed in laboratory experiments. Quite recently however, it was suggested that the concept of -symmetry could be physically realized within the framework of classical optics. This proposal has, in turn, stimulated extensive investigations and research studies related to -symmetric Optics and paved the way for the first experimental observation of -symmetry breaking in any physical system. In this paper, we present recent results regarding -symmetric Optic
- …