Many-particle quantum graphs: A review
arXiv:1805.00725 · doi:10.1007/978-3-030-44097-8
Abstract
In this paper we review recent work that has been done on quantum many-particle systems on metric graphs. Topics include the implementation of singular interactions, Bose-Einstein condensation, sovable models and spectral properties of some simple models in connection with superconductivity in wires.
References in corpus (19)
- One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
- Periodic Orbit Theory and Spectral Statistics for Quantum Graphs
- The trace formula for quantum graphs with general self adjoint boundary conditions
- Quantum Fields on Star Graphs
- Quantum graphs with singular two-particle interactions
- Quantum graphs with two-particle contact interactions
- Finite propagation speed and causal free quantum fields on networks
- Exact results for the one-dimensional many-body problem with contact interaction: Including a tunable impurity
- Quantum graphs and the integer quantum Hall effect
- On a two-particle bound system on the half-line
- Long-lived resonances at mirrors
- Exactly solvable interacting two-particle quantum graphs
- Two particles on a star graph I
- Two interacting particles on the half-line
- On pairs of interacting electrons in a quantum wire
- Instability of Bose-Einstein condensation on quantum graphs under repulsive perturbations
- On bound electron pairs in a quantum wire
- Two particles on a star graph II
- Zero modes of quantum graph Laplacians and an index theorem