QuantumBilliards.jl: An extensible, user friendly, high-performance Julia library for the large scale computation of spectra and eigenstates of quantum billiards and related problems
Abstract
We present QuantumBilliards.jl, an open-source Julia library providing a suite of numerical solvers for the two-dimensional interior Helmholtz eigenproblem with Dirichlet boundary conditions, a paradigmatic model in quantum chaos. The library implements conventional wavenumber-sweep techniques together with several accelerated eigensolvers: the Vergini--Saraceno scaling method, the expanded boundary integral method (EBIM), Beyn's contour-integral method, and the Compact Rational Krylov (CORK) method. It provides a common framework for constructing billiard geometries, exploiting discrete symmetries, computing eigenvalues and eigenstates, and treating smooth, cornered, and multiply connected domains. The library further includes reconstruction of eigenfunctions from boundary normal derivatives and the computation of Poincaré--Husimi (PH) phase-space representations. Available at: https://github.com/Quantum-Chaos-Julia/QuantumBilliards.jl.
Related
- Why finite-size non-Hermitian eigenvalues can miss asymptotic eigenstates in topological physics
- Accessing Chern Numbers From Bloch Eigenstates Singularities
- Generalized η-pairing eigenstates in three-component Hubbard models under a transverse field
- Real-space construction and selection rules of center-of-mass momentum eigenstates in two-dimensional many-body lattices
- Tripartite entanglement in chaotic eigenstates
BibTeX
@misc{orel2026quantumbilliardsjl,
title = {{QuantumBilliards.jl: An extensible, user friendly, high-performance Julia library for the large scale computation of spectra and eigenstates of quantum billiards and related problems}},
author = {Matic Orel and Črt Lozej},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32605},
eprint = {2610.32605},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32605},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - QuantumBilliards.jl: An extensible, user friendly, high-performance Julia library for the large scale computation of spectra and eigenstates of quantum billiards and related problems
AU - Matic Orel
AU - Črt Lozej
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32605
UR - https://arxiv.org/abs/2610.32605
AB - We present QuantumBilliards.jl, an open-source Julia library providing a suite of numerical solvers for the two-dimensional interior Helmholtz eigenproblem with Dirichlet boundary conditions, a paradigmatic model in quantum chaos. The library implements conventional wavenumber-sweep techniques together with several accelerated eigensolvers: the Vergini--Saraceno scaling method, the expanded boundary integral method (EBIM), Beyn's contour-integral method, and the Compact Rational Krylov (CORK) method. It provides a common framework for constructing billiard geometries, exploiting discrete symmetries, computing eigenvalues and eigenstates, and treating smooth, cornered, and multiply connected domains. The library further includes reconstruction of eigenfunctions from boundary normal derivatives and the computation of Poincaré--Husimi (PH) phase-space representations. Available at: https://github.com/Quantum-Chaos-Julia/QuantumBilliards.jl.
ER -