A. Som: INVESTIGATING INTERACTIONS: A STUDY OF CLASSICAL AND QUANTUM PHENOMENA IN COMPLEX SYSTEMS

This thesis explores a range of quantum and classical phenomena, focusing on the interactions and dynamic behaviors within distinct physical systems. The first part delves into the Casimir effect, investigating quantum fluctuations and electromagnetic field interactions at the nanoscale. The second section transitions to the study of superconducting Nickelates, where we use models such as the Periodic Anderson Model (PAM), to explore the emergence of unconventional superconductivity. The focus is on the interplay between electronic correlations, orbital hybridization, and dimensionality, which drive the complex behavior of these materials. Through functional Renormalization Group (fRG) techniques, the study provides a deeper understanding of the role of hybridization in the superconducting properties of Nickelates. The final part of the thesis investigates classical coupled oscillators, studying the interactions and synchronization behaviors in systems of multiple oscillators. This classical model provides an important contrast to the quantum systems studied earlier and helps to bridge the gap between quantum mechanics and classical physics through the exploration of emergent behaviors in both frameworks. Together, these works offer a comprehensive investigation into the interactions that govern both quantum and classical systems, providing new perspectives on phenomena that span from nanoscale quantum effects to macroscopic classical dynamics.