English
Related papers

Related papers: Scattering zippers and their spectral theory

200 papers

In a finite-dimensional Euclidian space we consider a connected metric graph with the following property: each two cycles can have at most one common point. Such graphs are called A-graphs. On noncompact A-graph we consider a scattering…

Spectral Theory · Mathematics 2013-11-13 Mikhail Ignatyev

Given a self-adjoint operator H, a self-adjoint trace class operator V and a fixed Hilbert-Schmidt operator F with trivial kernel and co-kernel, using limiting absorption principle an explicit set of full Lebesgue measure is defined such…

Spectral Theory · Mathematics 2018-12-21 Nurulla Azamov

We develop direct and inverse scattering theory for one-dimensional Schroedinger operators with steplike potentials which are asymptotically close to different finite-gap periodic potentials on different half-axes. We give a complete…

Spectral Theory · Mathematics 2008-11-20 Anne Boutet de Monvel , Iryna Egorova , Gerald Teschl

The famous question of Mark Kac "Can one hear the shape of a drum?" addressing the unique connection between the shape of a planar region and the spectrum of the corresponding Laplace operator can be legitimately extended to scattering…

Quantum Physics · Physics 2012-07-27 Oleh Hul , Michał Ławniczak , Szymon Bauch , Adam Sawicki , Marek Kuś , Leszek Sirko

Quantum graphs can be extended to scattering systems when they are connected by leads to infinity. It is shown that for certain extensions, the scattering matrices of isospectral graphs are conjugate to each other and their poles…

Mathematical Physics · Physics 2016-01-19 Ram Band , Adam Sawicki , Uzy Smilansky

This paper proves new results on spectral and scattering theory for matrix-valued Schr\"odinger operators on the discrete line with non-compactly supported perturbations whose first moments are assumed to exist. In particular, a Levinson…

Mathematical Physics · Physics 2022-11-10 Miguel Ballesteros , Gerardo Franco Córdova , Ivan Naumkin , Hermann Schulz-Baldes

A version of scattering theory that was developed many years ago to treat nuclear scattering processes, has provided a powerful tool to study universality in scattering processes involving open quantum systems with underlying classically…

Chaotic Dynamics · Physics 2022-10-12 L. E. Reichl , G. Akguc

We develop direct scattering theory for one-dimensional Schr\"odinger operators with steplike potentials, which are asymptotically close to different Bohr almost periodic infinite-gap potentials on different half-axes.

Spectral Theory · Mathematics 2022-01-17 Katrin Grunert

The acoustic scattering operator on the real line is mapped to a Schr\"odinger operator under the Liouville transformation. The potentials in the image are characterized precisely in terms of their scattering data, and the inverse…

solv-int · Physics 2007-05-23 R. Beals , D. H. Sattinger , J. Szmigielski

We demonstrate the interest of combining Finite Element calculations with the Vector Partial Wave formulation (used in T-matrix and Mie theory) in order to characterize the electromagnetic scattering properties of isolated individual…

Computational Physics · Physics 2018-08-15 Guillaume Demésy , Brian Stout , Jean-Claude Auger

The theory of scattering of atom pairs in a periodic potential is presented for the case of different atoms. When the scattering dynamics is restricted to the lowest Bloch band of the periodic potential, a separation in relative and average…

Other Condensed Matter · Physics 2009-11-13 R. T. Piil , N. Nygaard , K. Molmer

We consider a multichannel wire with a disordered region of length $L$ and a reflecting boundary. The reflection of a wave of frequency $\omega$ is described by the scattering matrix $\mathcal{S}(\omega)$, encoding the probability…

Mathematical Physics · Physics 2020-10-07 Aurélien Grabsch , Christophe Texier

We review the spectral analysis and the time-dependent approach of scattering theory for manifolds with asymptotically cylindrical ends. For the spectral analysis, higher order resolvent estimates are obtained via Mourre theory for both…

Mathematical Physics · Physics 2011-08-26 S. Richard , R. Tiedra de Aldecoa

We present a one-dimensional scattering theory which enables us to describe a wealth of effects arising from the coupling of the motional degree of freedom of scatterers to the electromagnetic field. Multiple scattering to all orders is…

Quantum Physics · Physics 2009-05-07 André Xuereb , Peter Domokos , János Asbóth , Peter Horak , Tim Freegarde

This work deals with the functional model for a class of extensions of symmetric operators and its applications to the theory of wave scattering. In terms of Boris Pavlov's spectral form of this model, we find explicit formulae for the…

Mathematical Physics · Physics 2020-07-21 Kirill D. Cherednichenko , Alexander V. Kiselev , Luis O. Silva

For scattering systems consisting of a (family of) maximal dissipative extension(s) and a selfadjoint extension of a symmetric operator with finite deficiency indices, the spectral shift function is expressed in terms of an abstract…

Mathematical Physics · Physics 2007-12-20 Jussi Behrndt , Mark M. Malamud , Hagen Neidhardt

We consider the spectral theory for discrete Schr\"odinger operators on the hexagonal lattice and their inverse scattering problem. We give a procedure for reconstructing the compactly supported potential from the scattering matrix for all…

Spectral Theory · Mathematics 2011-10-19 Kazunori Ando

Methods from scattering theory are introduced to analyze random Schroedinger operators in one dimension by applying a volume cutoff to the potential. The key ingredient is the Lifshitz-Krein spectral shift function, which is related to the…

Mathematical Physics · Physics 2007-05-23 Vadim Kostrykin , Robert Schrader

We formulate the Schiffer's conjecture in spectral geometry in the context of scattering theory. The problem is equivalent to finding a non-trivial solution in an interior transmission problem. We compare the back-scattering data of the…

Analysis of PDEs · Mathematics 2016-05-18 Lung-Hui Chen

Scattering theory in the Gell-Mann and Goldberger formulation is slightly extended to render a Hamiltonian quantum mechanical description of the neutrino oscillations.

High Energy Physics - Phenomenology · Physics 2012-06-14 Stanisław D. Głazek , Arkadiusz P. Trawiński