Master's project seminar: Daniel van Dyk

Title:
Calculating Transition Rates via Quantum Normal Forms

Abstract:
This thesis investigates the application of normal forms for computing transition rates from a meta-stable potential well over an anharmonic barrier. The method of normal forms allows one to find approximate, local constants of motion around stationary points by performing a perturbative expansion on the level of the Hamiltonian. This facilitates the efficient study of local dynamics and quantities of perturbed systems, such as the energy spectrum and partition function. Classical normal forms (CNF) and its quantum mechanical analogue (QNF) are functionally introduced, along with traditional methods to compute the transition rate of non-interacting systems, such as the path integral (PI). The PI and QNF approaches are compared in calculating the partition function of a quartic-perturbed potential. Finally, the computational results of a QNF Mathematica script are presented for the transition rates of various interacting systems.