In the first part of this thesis, a stochastic adaptation of the microcanonical simulation method is applied to the numerical simulation of the Su-Schrieffer-Heeger Hamiltonian for polyacetylene, a one-dimensional polymer were fermion-boson interactions play a dominant role in the dynamics of the system. The pure microcanonical simulation method fails in the marginally ergodic case and a stochastic adaptation, the hybrid microcanonical method, is employed to resolve problems with ergodicity. The hybrid method is shown to be an efficient method for higher dimensional fermionic quantum systems. In the second part of this thesis, a numerical simulation of the evolution of a network of global cosmic strings in an expanding Robertson-Walker universe is carried out. The system is quenched through an order-disorder phase transition and the nature of the string distribution is examined. While the string distribution observed at the phase transition is in good agreement with earlier estimates, the simulation reveals that the dynamics of the strings are suppressed by interactions with the Goldstone field. The network decays by topological annihilation and no spatial correlations are observed at any point in the simulation.
- Pub Date:
- Physics: Condensed Matter, Physics: Astronomy and Astrophysics