Solvable model of a quantum particle in a detector

2019 ◽  
Vol 17 (08) ◽  
pp. 1941004
Author(s):  
David Gaspard ◽  
Jean-Marc Sparenberg
Keyword(s):  
3D Model ◽  
Quantum Particle ◽  
Scattering Problem ◽  
Solvable Model ◽  
Forward Direction ◽  
Perturbative Calculation ◽  
Spherical Waves ◽  
Track Formation ◽  
Small Influence ◽  
Stationary Scattering

The interaction of a quantum particle with a gaseous detector is studied in the quantum-mechanical state space of the particle-detector system by means of a simple stationary scattering 3D model. The particle is assumed to interact with [Formula: see text] two-level point-like scatterers depicting the atoms of the detector. Due to the contact interaction, the particle scatters off the atoms in isotropic spherical waves. Remarkably, the Lippmann–Schwinger equation of this multiple scattering problem can be exactly solved in a nonperturbative way. The aim is to analyze the influence of the initial microstate of the detector on the observed outcome, and to understand the mechanism of track formation in gaseous detectors. It is shown that the differential cross-section of excitation must be large enough in the forward direction to get the formation of tracks. In addition, the relatively small influence of atomic positions is highlighted. These results are explained through a perturbative calculation.

The Aharonov–Bohm effect and its stationary scattering states from the flat circular annulus U(1) holonomy

2014 ◽  
Vol 11 (10) ◽  
pp. 1450084
Author(s):  
Gabriel Y. H. Avossevou ◽  
Bernadin D. Ahounou
Keyword(s):  
Scattering Problem ◽  
Heisenberg Algebra ◽  
Scattering Data ◽  
Gauge Potential ◽  
Circular Annulus ◽  
Topological Quantum ◽  
Vector Gauge ◽  
Simply Connected ◽  
Aharonov Bohm ◽  
Stationary Scattering

In this paper we study the stationary scattering problem of the Aharonov–Bohm (AB) effect. To achieve this goal we construct a Hamiltonian from the most general representations of the Heisenberg algebra. Such representations are defined on a non-simply-connected manifold which we set as the flat circular annulus. By means of the von Neumann's self-adjoint extensions formalism, the scattering data are then provided. No solenoid is considered in this paper. The corresponding Hamiltonian is based on a topological quantum degree of freedom inherent in such representations. This variable stands for the magnetic vector gauge potential at quantum level. Our outcomes confirm the topological nature of this effect.

Numerical simulation of acoustic scattering from coaxial sound-penetrable spheres

2019 ◽  
Vol 14 (2) ◽  
pp. 115-124
Author(s):  
E.Sh. Nasibullaeva
Keyword(s):  
Radiation Source ◽  
Numerical Study ◽  
Numerical Technique ◽  
Scattering Problem ◽  
Acoustic Scattering ◽  
Computer Time ◽  
Fixed Number ◽  
Helmholtz Equations ◽  
Spherical Waves ◽  
Penetrable Spheres

This paper presents a generalisation of the mathematical model and numerical study of the acoustic scattering problem from multiple spheres in the case of spheres through which the wave passes and whose centers are located on the same axis (the case of sound-penetrable and coaxial spheres) under the action of spherical waves from a monopoly radiation source arbitrarily located in space. When solving the Helmholtz equations, a numerical technique based on the fast multipole method has been adapted for this task, which allows one to achieve high accuracy of the results obtained with minimal computer time. Comparison of the different approaches to truncation infinite series in the expansion showed the following: the result with a good degree of accuracy by a single calculation gives approach based on the truncation of all the rows with a fixed number in each expansion, and the result with a certain degree of accuracy gives an approach based on comparing two consecutive values of the sum of the series. A numerical parametric analysis of the pressure distribution inside and outside the spheres is carried out for various values of their radii, physical characteristics of the external and internal media, the number of spheres, the distances between the centers of the spheres, the frequency of exposure and the location of the monopole radiation source. It is shown that at certain values of the parameters, the appearance of zones of decrease or increase in pressure behind sound-penetrable spheres is possible. The obtained results will further allow to carry out test calculations to verify the general numerical algorithm for the case of a multitude of spheres arbitrarily located in space.

scholarly journals Defect localization by an extended laser source on a hemisphere

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Daniel Veira Canle ◽  
Joni Mäkinen ◽  
Richard Blomqvist ◽  
Maria Gritsevich ◽  
Ari Salmi ◽  
...  
Keyword(s):  
Acoustic Waves ◽  
Line Source ◽  
3D Model ◽  
Scattering Problem ◽  
Laser Line ◽  
Experimental Results ◽  
Laser Source ◽  
Fem Simulations ◽  
Specific Direction ◽  
Defect Localization

AbstractThe primary goal of this study is to localize a defect (cavity) in a curved geometry. Curved topologies exhibit multiple resonances and the presence of hotspots for acoustic waves. Launching acoustic waves along a specific direction e.g. by means of an extended laser source reduces the complexity of the scattering problem. We performed experiments to demonstrate the use of a laser line source and verified the experimental results in FEM simulations. In both cases, we could locate and determine the size of a pit in a steel hemisphere which allowed us to visualize the defect on a 3D model of the sample. Such an approach could benefit patients by enabling contactless inspection of acetabular cups.

VALIDATION OF ACOUSTIC MODELS FOR TIME-HARMONIC DISSIPATIVE SCATTERING PROBLEMS

2007 ◽  
Vol 15 (01) ◽  
pp. 95-121 ◽  
Author(s):  
ALFREDO BERMÚDEZ ◽  
LUIS HERVELLA-NIETO ◽  
ANDRÉS PRIETO ◽  
RODOLFO RODRÍGUEZ
Keyword(s):  
Porous Medium ◽  
Finite Elements ◽  
Scattering Problem ◽  
Approximate Model ◽  
Scattering Problems ◽  
Acoustic Models ◽  
Spherical Waves ◽  
Time Harmonic ◽  
Medium System ◽  
Impedance Condition

The aim of this paper is to study the time-harmonic scattering problem in a coupled fluid-porous medium system. We consider two different models for the treatment of porous materials: the Allard–Champoux equations and an approximate model based on a wall impedance condition. Both models are compared by computing analytically their respective solutions for unbounded planar obstacles, considering successively plane and spherical waves. A numerical method combining an optimal bounded PML and finite elements is also introduced to compute the solutions of both problems for more general axisymmetric geometries. This method is used to compare the solutions for a spherical absorber.

RECIPROCITY RELATIONS FOR A CONDUCTIVE SCATTERER WITH A CHIRAL CORE IN QUASI-STATIC FORM

2018 ◽  
Vol 60 (1) ◽  
pp. 86-94
Author(s):  
C. E. ATHANASIADIS ◽  
E. S. ATHANASIADOU ◽  
S. DIMITROULA
Keyword(s):  
Electromagnetic Waves ◽  
Scattering Problem ◽  
Spherical Wave ◽  
Point Sources ◽  
Scattering Problems ◽  
Spherical Waves ◽  
Incident Plane ◽  
Reciprocity Relations ◽  
Static Form ◽  
Stationary Approximation

We analyse a scattering problem of electromagnetic waves by a bounded chiral conductive obstacle, which is surrounded by a dielectric, via the quasi-stationary approximation for the Maxwell equations. We prove the reciprocity relations for incident plane and spherical electric waves upon the scatterer. Mixed reciprocity relations have also been proved for a plane wave and a spherical wave. In the case of spherical waves, the point sources are located either inside or outside the scatterer. These relations are used to study the inverse scattering problems.

Generation of a 3D model to better mimic NAFLD in vitro

2016 ◽  
Vol 54 (12) ◽  
pp. 1343-1404
Author(s):  
LS Spitzhorn ◽  
MA Kawala ◽  
J Adjaye
Keyword(s):  
3D Model
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