Exponential decay of scattering coefficients

We study an aspect of the following general question: which properties of a signal can be characterized by its scattering transform? We show that the energy contained in high order scattering coefficients is upper bounded by the energy contained in the high frequencies of the signal. This result links the decay of the scattering coefficients of a signal with the decay of its Fourier transform. Additionally, it allows to generalize some results of Mallat (2012), by relaxing the admissibility condition on the wavelet family

Scattering Theory for Jacobi Operators with General Steplike Quasi-Periodic Background

We develop direct and inverse scattering theory for Jacobi operators with steplike coefficients which are asymptotically close to different finite-gap quasi-periodic coefficients on different sides. We give a complete characterization of the scattering data, which allow unique solvability of the inverse scattering problem in the class of perturbations with finite first moment.Comment: 23 page

Exploring matter wave scattering by means of the phase diagram

For matter wave scattering from passive quantum obstacles, we propose a phase diagram in terms of phase and modulus of scattering coefficients to explore all possible directional scattering patterns. In the phase diagram, we can not only have the physical bounds on scattering coefficients for all channels, but also indicate the competitions among absorption, extinction, and scattering cross sessions. With help of this phase diagram, we discuss different scenarios to steer scattering probability distribution, through the interference between $s$- and $p$-channels. In particular, we reveal the required conditions to implement a quantum scatterer, i.e., a quantum dot in semiconductor matrix, with a minimum (or zero) value in the scattering probability toward any direction. Our results provide a guideline in designing quantum scatterers with controlling and sensing matter waves.Comment: 6 pages, 3 figure

Scattering matrices and expansion coefficients of Martian analogue palagonite particles

We present measurements of ratios of elements of the scattering matrix of Martian analogue palagonite particles for scattering angles ranging from 3 to 174 degrees and a wavelength of 632.8 nm. To facilitate the use of these measurements in radiative transfer calculations we have devised a method that enables us to obtain, from these measurements, a normalized synthetic scattering matrix covering the complete scattering angle range from 0 to 180 degrees. Our method is based on employing the coefficients of the expansions of scattering matrix elements into generalized spherical functions. The synthetic scattering matrix elements and/or the expansion coefficients obtained in this way, can be used to include multiple scattering by these irregularly shaped particles in (polarized) radiative transfer calculations, such as calculations of sunlight that is scattered in the dusty Martian atmosphere.Comment: 34 pages 7 figures 1 tabl