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arXiv:2610.32605

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

Matic Orel, Črt Lozej

quant-phphysics.comp-phSubmitted Oct 23, 2026• Announced Oct 26, 2026
arXivHTMLPDF

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.

Comments
53 pages, 19 figures

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