The Single-Particle density of States, Bound States, Phase-Shift Flip, and a Resonance in the Presence of an Aharonov-Bohm Potential

Abstract

Both the nonrelativistic scattering and the spectrum in the presence of the Aharonov-Bohm potential are analyzed. The single-particle density of states (DOS) for different self-adjoint extensions is calculated. The DOS provides a link between different physical quantities and is a natural starting point for their calculation. The consequences of an asymmetry of the S matrix for the generic self-adjoint extension are examined. I. Introduction II. Impenetrable flux tube and the density of states III. Penetrable flux tube and self-adjoint extensions IV. The S matrix and scattering cross sections V. The Krein-Friedel formula and the resonance VI. Regularization VII. The R --> 0 limit and the interpretation of self-adjoint extensions VIII. Energy calculations IX. The Hall effect in the dilute vortex limit X. Persistent current of free electrons in the plane pierced by a flux tube XI. The 2nd virial coefficient of nonrelativistic interacting anyons XII. Discussion of the results and open questions

68 pages, plain latex, 7 figures, 3 references and one figure added plus a few minor text corrections

References in corpus (5)

• Density-of-States Calculations and Multiple-Scattering Theory for Photons
• Perturbative Renormalization in Quantum Mechanics
• The Aharonov-Casher Theorem and the Axial Anomaly in the Aharonov-Bohm Potential
• Persistent Current of Free Electrons in the Plane
• The single-particle density of states and a resonance in the Aharonov-Bohm potential

Cited by in corpus (22)

• Quasiparticles and Vortices in Unconventional Superconductors
• Electronic states and quantum transport in double-wall carbon nanotubes
• Magnetic Force Exerted by the Aharonov-Bohm Line (II)
• Hamiltonian self-adjoint extensions for (2+1)-dimensional Dirac particles
• Anomalous electron trapping by localized magnetic fields
• Energy-pressure relation for low-dimensional gases
• Anomalous Defects and Their Quantized Transverse Conductivities
• Statistical Mechanics of an Ideal Gas of Non-Abelian Anyons
• Hall Conductivity for Two Dimensional Magnetic Systems
• Hidden superconformal symmetry of spinless Aharonov-Bohm system
• Supersymmetries of the spin-1/2 particle in the field of magnetic vortex, and anyons
• Density of states of relativistic and nonrelativistic two-dimensional electron gases in a uniform magnetic and Aharonov-Bohm fields
• Persistent Currents and Magnetization in two-dimensional Magnetic Quantum Systems
• Aharonov-Bohm effect in relativistic and nonrelativistic 2D electron gas: a comparative study
• Quantum mechanics of an electron in a homogeneous magnetic field and a singular magnetic flux tube
• Electron trapping by a current vortex
• Diagonal deformations of thin center vortices and their stability in Yang-Mills theories
• Bound states of a spin-1/2 charged particle in a magnetic flux tube
• Second Virial Coefficient of Anyons without Hard Core
• Semiclassical Theory for Two-anyon System
• Several remarks on ``Comments'' by A. Moroz
• Comments on ``Differential cross section for Aharonov-Bohm effect with nonstandard boundary conditions''