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

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.

32 pages

References in corpus (7)

• Quantum Fields on Star Graphs
• Quantum statistics on graphs
• Avoiding Ultraviolet Divergence by Means of Interior-Boundary Conditions
• Hamiltonians Without Ultraviolet Divergence for Quantum Field Theories
• Many-particle quantum graphs and Bose-Einstein condensation
• Two particles on a star graph I
• Two particles on a star graph II

Cited by in corpus (14)

• On Nelson-type Hamiltonians and abstract boundary conditions
• Avoiding Ultraviolet Divergence by Means of Interior-Boundary Conditions
• Particle Creation at a Point Source by Means of Interior-Boundary Conditions
• Hamiltonians Without Ultraviolet Divergence for Quantum Field Theories
• On Bohmian Mechanics, Particle Creation, and Relativistic Space-Time: Happy 100th Birthday, David Bohm!
• Consistency of multi-time Dirac equations with general interaction potentials
• Multi-time formulation of particle creation and annihilation via interior-boundary conditions
• Bohmian Trajectories for Hamiltonians with Interior-Boundary Conditions
• Complex Charges, Time Reversal Asymmetry, and Interior-Boundary Conditions in Quantum Field Theory
• Interior-Boundary Conditions for Many-Body Dirac Operators and Codimension-1 Boundaries
• Hamiltonians for polaron models with subcritical ultraviolet singularities
• Interior-Boundary Conditions for the Dirac Equation at Point Sources in 3 Dimensions
• Interior-Boundary Conditions for Schrodinger Operators on Codimension-1 Boundaries
• Boundary Conditions that Remove Certain Ultraviolet Divergences