Highly efficient quantum spin dynamics simulation algorithms - Edwards, L (2014)
Spin dynamics simulations are used to gain insight into important magnetic resonance experiments in the fields of chemistry, biochemistry, and physics. Presented in this thesis are investigations into how to accelerate these simulations by making them more efficient. Chapter 1 gives a brief introduction to the methods of spin dynamics simulation used in the rest of the thesis. The `exponential scaling problem' that formally limits the size of spin system that can be simulated is described. Chapter 2 provides a summary of methods that have been developed to overcome the exponential scaling problem in liquid state magnetic resonance. The possibility of utilizing the multiple processors prevalent in modern computers to accelerate spin dynamics simulations provides the impetus for the investigation found in Chapter 3. A number of different methods of parallelization leading to acceleration of spin dynamics simulations are derived and discussed. It is often the case that the parameters defining a spin system are time-dependent. This complicates the simulation of the spin dynamics of the system. Chapter 4 presents a method of simplifying such simulations by mapping the spin dynamics into a larger state space. This method is applied to simulations incorporating mechanical spinning of the sample with powder averaging. In Chapter 5, implementations of several magnetic resonance experiments are detailed. In so doing, use of techniques developed in Chapters 2 and 3 are exemplified. Further, specific details of these experiments are utilized to increase the efficiency of their simulation.