Development and Application of New Numerical Extensions to the Coupled Coherent States Family of Multidimensional Quantum Dynamics Methods

The coupled coherent states method has demonstrated itself as an accurate and efficient method of studying the quantum dynamics of various systems. In recent years, its applicability has been extended by incorporating a number of new numerical expansions and modifications to generate a closely related family of methods. In this thesis, two new augmentations are developed to further broaden the scope of problems that are able to be treated. The first of these is a 2-layer extension of coupled coherent states, capable of providing an increased mathematical description of a degree or degrees of freedom within a quantum mechanical system, as well as beneficial numerical and scalability properties. The newly developed method is tested on a model system-bath Hamiltonian consisting of a tunnelling mode governed by an asymmetric double well potential coupled to a harmonic bath. It is found to compare well to previous methods of studying the Hamiltonian, as well as a benchmark calculation on the system conducted in this thesis, and demonstrate the beneficial numerical and scalability properties expected. The second development is to extend coupled coherent states to treat systems of indistinguishable bosons in the second quantisation representation. The method is tested on the same Hamiltonian as the 2-layer coupled coherent states scheme, where the harmonic bath is second quantised as it is comprised of oscillators of the same frequency, so they may be thought of as indistinguishable. Exploiting this symmetry property is found to be extremely advantageous, with remarkable agreement to the benchmark calculation. The method is then tested on a model Hamiltonian consisting of 100 bosons in a shifted harmonic trap, with oscillations in the 1-body density calculated. The results are found to compare favourably with a multiconfigurational time-dependent Hartree for bosons calculation that is equivalent to the Gross-Pitaevskii equation, providing impetus for future studies on systems of Bose-Einstein condensates. The existing ab initio multiple cloning extension of coupled coherent states for nonadiabatic dynamics is also used to study the ultrafast photodissociation of 2-ethylpyrrole. The results are compared to experimental data, and a novel insight into the dissociation mechanism is obtained, with it shown to be composed of a two step process. Firstly, molecules that are able to dissociate immediately over the barrier along the N-H coordinate do so in < 50 fs, and this is followed by a second slower dissociation process from molecules that must sample the potential energy surface before finding a way around the barrier. This is not observed experimentally due to the temporal widths of the laser pulses obscuring the dynamics in the < 50 fs window.