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

TL;DR

This paper investigates the effects of the Aharonov-Bohm potential on single-particle states, scattering, and related physical phenomena, emphasizing the role of self-adjoint extensions and their impact on the density of states and resonances.

Contribution

It provides a comprehensive analysis of the density of states, scattering matrix asymmetries, and resonances in the presence of an Aharonov-Bohm flux, including new insights into self-adjoint extensions and their physical implications.

Findings

Calculated the density of states for various self-adjoint extensions.

Identified the impact of S matrix asymmetry on physical quantities.

Analyzed the resonance phenomena and their relation to the Krein-Friedel formula.

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