Charged particles interaction in both a finite volume and a uniform magnetic field II: topological and analytic properties of a magnetic system

TL;DR

This paper explores the topological characteristics and analytic properties of charged particles in a finite volume under a uniform magnetic field, highlighting edge states and their spectral signatures.

Contribution

It introduces a detailed analysis of topological features and edge state solutions in a finite magnetic system, extending understanding of such quantum systems.

Findings

Edge states appear within energy gaps, indicating non-trivial topology.

Analytic solutions reveal complex plane properties of two-body systems.

Topological features are characterized through spectral and edge state analysis.

Abstract

In present work, we discuss some topological features of charged particles interacting a uniform magnetic field in a finite volume. The edge state solutions are presented, as a signature of non-trivial topological systems, the energy spectrum of edge states show up in the gap between allowed energy bands. By treating total momentum of two-body system as a continuous distributed parameter in complex plane, the analytic properties of solutions of finite volume system in a magnetic field is also discussed.