79,276 research outputs found
Scattering and inverse scattering for nonlinear quantum walks
We study large time behavior of quantum walks (QWs) with self-dependent
(nonlinear) coin. In particular, we show scattering and derive the reproducing
formula for inverse scattering in the weak nonlinear regime. The proof is based
on space-time estimate of (linear) QWs such as dispersive estimates and
Strichartz estimate. Such argument is standard in the study of nonlinear
Schr\"odinger equations and discrete nonlinear Schr\"odinger equations but it
seems to be the first time to be applied to QW.Comment: 18 pages, text overlap with arXiv:1711.0062
Inverse scattering for reflection intensity phase microscopy
Reflection phase imaging provides label-free, high-resolution characterization of biological samples, typically using interferometric-based techniques. Here, we investigate reflection phase microscopy from intensity-only measurements under diverse illumination. We evaluate the forward and inverse scattering model based on the first Born approximation for imaging scattering objects above a glass slide. Under this design, the measured field combines linear forward-scattering and height-dependent nonlinear back-scattering from the object that complicates object phase recovery. Using only the forward-scattering, we derive a linear inverse scattering model and evaluate this model's validity range in simulation and experiment using a standard reflection microscope modified with a programmable light source. Our method provides enhanced contrast of thin, weakly scattering samples that complement transmission techniques. This model provides a promising development for creating simplified intensity-based reflection quantitative phase imaging systems easily adoptable for biological research.https://arxiv.org/abs/1912.07709Accepted manuscrip
Transmission of matter wave solitons through nonlinear traps and barriers
The transmissions of matter wave solitons through linear and nonlinear
inhomogeneities induced by the spatial variations of the trap and the
scattering length in Bose-Einstein condensates are investigated. New phenomena,
such as the enhanced transmission of a soliton through a linear trap by a
modulation of the scattering length, are exhibited. The theory is based on the
perturbed Inverse Scattering Transform for solitons, and we show that radiation
effects are important. Numerical simulations of the Gross-Pitaevskii equation
confirm the theoretical predictions.Comment: 6 pages, 4 figure
On Whitham theory for perturbed integrable equations
Whitham theory of modulations is developed for periodic waves described by
nonlinear wave equations integrable by the inverse scattering transform method
associated with matrix or second order scalar spectral problems. The
theory is illustrated by derivation of the Whitham equations for perturbed
Korteweg-de Vries equation and nonlinear Schr\"odinger equation with linear
damping.Comment: 17 pages, no figure
Efficient Inversion of Multiple-Scattering Model for Optical Diffraction Tomography
Optical diffraction tomography relies on solving an inverse scattering
problem governed by the wave equation. Classical reconstruction algorithms are
based on linear approximations of the forward model (Born or Rytov), which
limits their applicability to thin samples with low refractive-index contrasts.
More recent works have shown the benefit of adopting nonlinear models. They
account for multiple scattering and reflections, improving the quality of
reconstruction. To reduce the complexity and memory requirements of these
methods, we derive an explicit formula for the Jacobian matrix of the nonlinear
Lippmann-Schwinger model which lends itself to an efficient evaluation of the
gradient of the data- fidelity term. This allows us to deploy efficient methods
to solve the corresponding inverse problem subject to sparsity constraints
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