Date of Award

December 2018

Degree Type


Degree Name

Doctor of Philosophy (PhD)




Arindam Chakraborty

Subject Categories

Physical Sciences and Mathematics


The focus of this work is to develop theoretical methods that will accurately describe electron-electron and electron-hole correlation in nanoparticles using many-body diagrammatic techniques. Diagrammatic representation is a more complex representation of quantum mechanics, however, it becomes a more advantageous representation in its application to this work due to its ease of use. Diagrammatic techniques are essential to the ve methods presented here as they prove to be pivotal in theoretical development as well as providing useful information in extracting and visualizing fundamental physics to make useful approximations to the methods. In the projected congruent transformed Hamiltonian method with partial innite order summation of diagrams (PCTH-PIOS), diagrammatic summation approach was used. In the geminal projected conguration interaction (GPCI) method, diagrammatic factorization techniques were used. In the geminal screened electron-hole interaction kernel (GSIK) method, we conclude that only linked diagrams contribute to the exciton binding energy. The approximation is made to only include rst order diagrams which captures the essential physics of the electron-hole interaction. In the composite control-variate stratied sampling (CCSS) method the calculation of the vertices of the diagrams using stratied sampling. Lastly we investigate the eect of electromagnetic (EM) eld on the generation of 2e-2h states from 1e-1h states. In this work, time independent diagrams are calculated once and used for the rest of the calculation. Diagrammatic techniques are essential to the theoretical development of the methods in this work for understanding the optical and electronic properties of nanoparticles.


Open Access