Some Studies On Two-Body Random Matrix Ensembles

TL;DR

This paper analyzes embedded Gaussian ensembles (EGEs), which model two-body interactions in finite quantum systems, to understand their properties and relevance for systems like nuclei, atoms, and quantum dots.

Contribution

It systematically studies various physically relevant EGEs with symmetries using multiple measures to characterize finite interacting quantum systems.

Findings

Identification of key properties of EGEs with symmetries

Analysis of measures relevant for quantum systems

Insights into the structure of two-body random matrix ensembles

Abstract

In finite many-body quantum systems such as nuclei, atoms, mesoscopic systems like quantum dots and small metallic grains, interacting spin systems modeling quantum computing core and BEC, the interparticle interactions are essentially two-body in nature. Therefore, it is more appropriate to represent the complex Hamiltonian of these systems by random ensembles that incorporate the two-body nature of interactions. These ensembles are generically called embedded Gaussian ensembles (EGEs). The aim of the present thesis is to identify and systematically analyze many different physically relevant EGEs with symmetries by considering a variety of quantities and measures that are important for isolated finite interacting quantum systems.