Stationary Scattering in Planar Confining Geometries

2016 ◽  
pp. 59-101
Author(s):  
Christian V. Morfonios ◽  
Peter Schmelcher
Keyword(s):  
Stationary Scattering

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.

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.

Relativistic Lippmann–Schwinger equation as an integral equation

2019 ◽  
Vol 31 (09) ◽  
pp. 1950032
Author(s):  
Lev Sakhnovich
Keyword(s):  
Integral Equation ◽  
Dirac Equation ◽  
Explicit Form ◽  
Scattering Problems ◽  
Relativistic Case ◽  
Limit Values ◽  
Stationary Scattering

The relativistic Lippmann–Schwinger equation was earlier formulated in terms of the limit values of the corresponding resolvent. In the present paper, we write down the limit values of the resolvent in an explicit form, and so the relativistic Lippmann–Schwinger equation is presented as an integral equation. Using this integral equation, we investigate the stationary scattering problems (relativistic case, Dirac equation). We consider the dynamical scattering problems (relativistic case, Dirac equation) as well.

Linear passive stationary scattering systems with Pontryagin state spaces

2006 ◽  
Vol 279 (13-14) ◽  
pp. 1396-1424 ◽  
Author(s):  
D. Z. Arov ◽  
J. Rovnyak ◽  
S. M. Saprikin
Keyword(s):  
State Spaces ◽  
Scattering Systems ◽  
Stationary Scattering
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