Dynamics of complex physical systems
This project covers the study of different physical systems, based on substantially different principles, from quantum mechanics to fluid dynamics. The main unifying theme is their dynamical (time-dependent) aspect, along with the fact that they are computationally intensive. The reason for grouping them in a single application is simply that they correspond to different research projects I am involved in in parallel. The first part concerns the simulation of the dynamics of ions in electrostatic traps, such as the Paul trap. By solving the time-dependent Schrödinger equation in one to three dimensions, we can get the full wavepacket dynamics, that is, the centre-of-mass motion of the ion in the time-periodic trapping potential. Trapped ions are currently used in experiments aimed at developing quantum information processing, and an investigation of the quantum dynamics of the ions in the trap, and its eventual control using laser fields, will be of great interest to the field of quantum computing. The present work concerns mostly the dynamics of molecular ions and their interaction with short laser pulses. The second part is aimed at the study the behavior of dilute gases of cold atoms at temperatures below the millikelvin. The project concerns the dynamics of atoms in optical lattices, which are spatially-modulated potentials created from the interference of laser beams. The objective here is to get a time-dependent picture of atoms trapped in optical lattices and to look for anomalous statistics in the distribution of high-momentum atoms. In addition, the effect of gravity, which corresponds here to a tilt of the optical lattice potential, is studied. The atom + optical lattice system can be related to a very general problem in physics, that of a Brownian particle moving in a periodic potential, and one of the aims of this work is to see how the actual experimental setup can be used as an actual implementation of the system and, therefore, as a testbed for fundamental statistical physics. The simulations consists in solving the Fokker-Planck equation for a single atom in a lattice, in a semi-classical approach, where only the internal state of the atom is treated quantum-mechanically. A third part of the project concerns the dynamics of combustion in premixed gases. In particular, we simulate the propagation of frame fronts in narrow tubes, looking at different aspects such as the acceleration of the flame front, its curvature, the development of instabilities and the deflagration to detonation transition. Current work focuses mainly on the role of cold tube walls on flame acceleration and the effect of obstacles. The dynamics are obtained by solving the Navier-Stokes combustion equations.