Bill2d - a software package for classical two-dimensional Hamiltonian systems

TL;DR

Bill2d is a versatile C++ software package designed for simulating and analyzing two-dimensional classical Hamiltonian systems, supporting various boundary conditions, external fields, and particle interactions, with tools for key dynamical quantities.

Contribution

The paper introduces Bill2d, a modern, efficient, and modular C++ package that facilitates classical simulations of 2D Hamiltonian systems with extensive features and user support.

Findings

Supports billiard and diffusion problems with multiple particles

Calculates Poincaré sections, survival probabilities, and diffusion coefficients

Designed for ease-of-use, efficiency, and extensibility

Abstract

We present Bill2d, a modern and efficient C++ package for classical simulations of two-dimensional Hamiltonian systems. Bill2d can be used for various billiard and diffusion problems with one or more charged particles with interactions, different external potentials, an external magnetic field, periodic and open boundaries, etc. The software package can also calculate many key quantities in complex systems such as Poincar\'e sections, survival probabilities, and diffusion coefficients. While aiming at a large class of applicable systems, the code also strives for ease-of-use, efficiency, and modularity for the implementation of additional features. The package comes along with a user guide, a developer's manual, and a documentation of the application program interface (API).