Mathematical Analysis and Derivation of the Arrabal-Zurek Decoherence Formula

This thesis presents a mathematical analysis and derivation of the Arrabal-Zurek Decoherence Formula, an extension of Wojciech Zurek's original decoherence theory. The formula models how quantum coherence decays over time, incorporating velocity as a critical parameter in the decoherence process. Starting with a review of Zurek's decoherence model, the formula is extended to account for velocity-dependent decoherence. Through dimensional analysis, consistency checks, and exploration ofits behavior under limiting cases (e.g., low and high velocities, short and long times), this work demonstrates that the Arrabal-Zurek formula provides a robust framework for understanding the transition of quantum systems to classical behavior at critical velocities. The thesis also explores potential experimental applications in fields such as quantum computing, particle physics, and cosmology.