0000000000381581
AUTHOR
Janne Solanpää
Nonlinear dynamics and chaos in classical Coulomb-interacting many-body billiards
Chaos and nonlinear dynamics of single-particle Hamiltonian systems have been extensively studied in the past; however, less is known about interacting many-body systems in this respect even though all physical systems include particle-particle interactions in one way or another. To study Hamiltonian chaos, two-dimensional billiards are usually employed, and due to the realization of billiards in semiconductor quantum dots, the electrostatic Coulomb interaction is the natural choice for the interparticle interaction. Yet, surprisingly little is known about chaos and nonlinear dynamics of Coulomb-interacting many-body billiards. To address the challenging problems of interacting many-body bi…
Bill2d - a software package for classical two-dimensional Hamiltonian systems
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 Poincare 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 use…
Coulomb-interacting billiards in circular cavities
We apply a molecular dynamics scheme to analyze classically chaotic properties of a two-dimensional circular billiard system containing two Coulomb-interacting electrons. As such, the system resembles a prototype model for a semiconductor quantum dot. The interaction strength is varied from the noninteracting limit with zero potential energy up to the strongly interacting regime where the relative kinetic energy approaches zero. At weak interactions the bouncing maps show jumps between quasi-regular orbits. In the strong-interaction limit we find an analytic expression for the bouncing map. Its validity in the general case is assessed by comparison with our numerical data. To obtain a more …
Many-particle dynamics and intershell effects in Wigner molecules
We apply classical molecular dynamics within the velocity Verlet algorithm to examine the formation dynamics of Wigner crystals in two-dimensional harmonic oscillators. Using a large ensemble of initial conditions as well as different freezing mechanisms, we obtain reliable information on the energies and probabilities of stable and metastable configurations, their formation dynamics, and their stability. Wigner-crystal configurations of up to 30 particles are presented and the dynamics of transition processes, e.g., intershell effects, are analyzed.