English
Related papers

Related papers: High-Velocity Estimates for the Scattering Operato…

200 papers

We investigate the transport through a quantum ring, a dot and a barrier embedded in a nanowire in a homogeneous perpendicular magnetic field. To be able to treat scattering potentials of finite extent in magnetic field we use a mixed…

Mesoscale and Nanoscale Physics · Physics 2007-05-23 Vidar Gudmundsson , Yu-Yu Lin , Chi-Shung Tang , Valeriu Moldoveanu , Jens Hjorleifur Bardarson , Andrei Manolescu

This work studies existence and regularity questions for attracting invariant tori in three dimensional dissipative systems of ordinary differential equations. Our main result is a constructive method of computer assisted proof which…

Dynamical Systems · Mathematics 2020-01-14 Maciej J. Capinski , Emmanuel Fleurantin , Jason D. Mireles James

We show that for a one-dimensional Schr\"odinger operator with a potential whose first moment is integrable the scattering matrix is in the unital Wiener algebra of functions with integrable Fourier transforms. Then we use this to derive…

Analysis of PDEs · Mathematics 2016-06-30 Iryna Egorova , Elena Kopylova , Vladimir Marchenko , Gerald Teschl

For any positive real number $s$, we study the scattering theory in a unified way for the fractional Schr\"{o}dinger operator $H=H_0+V$, where $H_0=(-\Delta)^\frac s2$ and the real-valued potential $V$ satisfies short range condition. We…

Mathematical Physics · Physics 2021-04-12 Rui Zhang , Tianxiao Huang , Quan Zheng

We present, to the best of our knowledge, the first numerical algorithm for explicit, computable two-sided eigenvalue bounds for Schr\"odinger operators H = -Delta + V on R^N, N = 2,3, in the presence of both an unbounded potential and an…

Numerical Analysis · Mathematics 2026-05-07 Xuefeng Liu

We study the strongly singular volume integral equation that describes the scattering of time-harmonic electromagnetic waves by a penetrable obstacle. We consider the case of a cylindrical obstacle and fields invariant along the axis of the…

Analysis of PDEs · Mathematics 2015-09-30 Martin Costabel , Eric Darrigrand , Hamdi Sakly

We study the splitting of invariant manifolds of whiskered tori with two or three frequencies in nearly-integrable Hamiltonian systems. We consider 2-dimensional tori with a frequency vector $\omega=(1,\Omega)$ where $\Omega$ is a quadratic…

Dynamical Systems · Mathematics 2013-06-05 Amadeu Delshams , Marina Gonchenko , Pere Gutierrez

The hadronic quark structure is investigated in the frame of high energy electron proton scattering. A phenomenological model based on the Born approximation is used to calculate the transition matrix element for the quark system forming…

High Energy Physics - Phenomenology · Physics 2008-02-03 M. T. Hussein , N. M. Hassan

We consider the magnetic flux in a quantum mechanical superposition of two values and find that the Aharonov-Bohm effect interference pattern contains information about the nature of the superposition, allowing information about the state…

Quantum Physics · Physics 2014-02-12 Kaća Bradonjić , John D. Swain

In this paper we calculate the analytic expression of the phase time for the scattering of an electron off a complex square barrier. As is well known the (negative) imaginary part of the potential takes into account, phenomenologically, the…

Quantum Physics · Physics 2009-11-07 Fabio Raciti , Giovanni Salesi

We revisit the well known Bohr-Sommerfeld quantization rule (BS) of order 2 for a self-adjoint 1-D h-Pseudo-differential operator within the algebraic and microlocal framework of Helffer and Sjoestrand; BS holds precisely when Gram matrix…

Mathematical Physics · Physics 2026-01-13 Abdelwaheb Ifa , Michel Rouleux

Scattering theory has been suggested as a convenient method to identify topological phases of matter, in particular of disordered systems for which the Bloch band-theory approach is inapplicable. Here we examine this idea, employing as a…

Mesoscale and Nanoscale Physics · Physics 2024-03-14 Zhi-Hai Liu , O. Entin-Wohlman , A. Aharony , J. Q. You , H. Q. Xu

We study the real time dynamics of electron coherence in a double quantum dot two-terminal Aharonov-Bohm geometry, taking into account repulsion effects between the dots' electrons. The system is simulated by extending a numerically exact…

Mesoscale and Nanoscale Physics · Physics 2015-06-03 Salil Bedkihal , Dvira Segal

Stationary scattering problem (when the distance $r$ tends to infinity) and dynamical scattering problem (when the time $t$ tends to infinity) are considered for the 3D Schr\"odinger equation. A simple interconnection between the scattering…

Mathematical Physics · Physics 2019-05-21 Lev Sakhnovich

In this paper, we study the direct and inverse scattering of the Schr\"odinger equation in a three-dimensional planar waveguide. For the direct problem, we derive a resonance-free region and resolvent estimates for the resolvent of the…

Analysis of PDEs · Mathematics 2024-02-27 Yan Chang , Yukun Guo , Yue Zhao

We develop a complete stationary scattering theory for Schr\"odinger operators on $\mathbb R^d$, $d\ge 2$, with $C^2$ long-range potentials. This extends former results in the literature, in particular [Is1, Is2, II, GY], which all require…

Mathematical Physics · Physics 2024-08-07 K. Ito , E. Skibsted

We consider a Volovik's analog model for description of a topological defects in a superfluid and we investigate the scattering of quasiparticles in this background. The analog of the gravitational Aharonov-Bohm in this system is found. An…

General Relativity and Quantum Cosmology · Physics 2011-07-19 L. C. Garcia de Andrade , A. M. de M. Carvalho , C. Furtado

We prove the existence of scattering solutions for multidimensional magnetic Schr\"odinger equation which belong to the weighted Sobolev space H^1_s (R^n)(n=2,3) with some s < -1/2. As a consequence of this we formulate the direct Born…

Mathematical Physics · Physics 2013-03-25 Valery Serov , Jan Sandhu

The diagrammatic formalism and transport equation are conventionally considered as separate but complementary techniques to tackle the impurity scattering effect. To compare with the previous studies from the gauge-invariant kinetic…

Superconductivity · Physics 2022-10-25 F. Yang , M. W. Wu

Consider a time-harmonic elastic point source incident on a bounded obstacle which is embedded in an open space filled with a homogeneous and isotropic elastic medium. This paper is concerned with the inverse problem of recovering the…

Analysis of PDEs · Mathematics 2025-06-02 Chun Liu , Guanghui Hu , Tao Yin , Bo Zhang