Investigation of Random Matrix Theory for Statistical Mechanics and Quantum Physics Applications

Abstract

Due to its capability to explain large systems with chaotic behaviour, Random Matrix Theory (RMT) has drawn a lot of interest in the domains of Statistical Mechanics and Quantum Physics. Investigating RMT's uses in these fields is the main goal of this study.RMT offers a potent framework for studying the behaviour of sizable ensembles of interacting particles in statistical mechanics. RMT enables the examination of different physical features including energy spectra and correlation functions by using random matrices as models for Hamiltonians. Advancements in disciplines like condensed matter physics and nuclear physics have been made possible by the universality aspects of RMT, which allow for the comprehension of universal features seen in many-body systems.RMT is an essential tool for understanding the statistical behaviour of quantum systems in quantum physics, especially when there are strong interactions present. It gives scientists a useful tool for describing the energy states and wave functions of complicated quantum systems, including those with chaotic dynamics. Understanding of phenomena including quantum transport, quantum entanglement, and quantum chaos has benefited by the knowledge obtained from RMT.With this study, we hope to add to the body of knowledge on RMT's uses in quantum physics and statistical mechanics. It offers important insights into the behaviour of complex systems and paves the road for improvements in these domains by investigating the characteristics of random matrices and their relationships to physical systems.