Particle creation and annihilation at interior boundaries: One-dimensional models

TL;DR

This paper introduces interior-boundary conditions to model particle creation and annihilation in one-dimensional systems, providing explicit solutions and extending the framework to quantum graphs.

Contribution

It develops a comprehensive framework for particle creation and annihilation at boundaries using IBCs, including explicit spectral solutions and a quantum graph extension.

Findings

Derived explicit spectra and eigenfunctions.

Provided Green functions and spectral determinants.

Extended IBC framework to quantum graphs.

Abstract

We describe creation and annihilation of particles at external sources in one spatial dimension in terms of interior-boundary conditions (IBCs). We derive explicit solutions for spectra, (generalised) eigenfunctions, as well as Green functions, spectral determinants, and integrated spectral densities. Moreover, we introduce a quantum graph version of IBC-Hamiltonians.