Chintalpati Umashankar Shastry

In this project I am working under the supervision of Dr Andrea Rocco. My primary research investigates the emergence of irreversibility in statistical mechanics, with a particular emphasis on the role of multi-particle correlations within the Bogoliubov–Born–Green–Kirkwood–Yvon (BBGKY) hierarchy. This study rigorously explores how entropy functions arise from the molecular dynamics of systems exhibiting multiparticle correlations. I am presently developing a methodological framework to derive the appropriate functional form of the entropy function when the BBGKY hierarchy is truncated at a specified level.

Here I am undertaking the project under the supervision of Dr. Rocco, which centers on the application of the Renormalization Group (RG) approach to open quantum systems. This project advances the Non-Perturbative Renormalization Group (NPRG) analysis through the derivation of a generalized Wegner–Houghton equation that incorporates both dissipation and decoherence effects. Employing the Caldeira–Leggett model, I introduce a ζ-function framework to capture the influence of decoherence on quantum-classical transitions. This approach seeks to overcome the limitations of conventional methods by incorporating both dissipative and decoherence effects into the analysis of quantum-to-classical transitions. Future work aims to validate this framework and investigate its implications within the context of the Local Potential Approximation.

For my MSc dissertation, I investigated the Dirac equation for the hydrogen atom using finite basis expansion methods under the supervision of  Dr Paul Stevenson. The project focused on obtaining a matrix representation of the Dirac Hamiltonian within a finite set of basis spinors. While any infinite basis set can theoretically represent the Hamiltonian, improper kinetic balancing of the basis functions leads to the emergence of spurious energy states in the spectrum.

Two distinct methodologies were developed and analyzed: the Basis Expansion Method and the Variational Method. In the Basis Expansion Method, the matrix elements were calculated by taking the inner product of kinetically balanced Dirac basis spinors with the Dirac Hamiltonian. In contrast, the Variational Method involved expanding the large component in terms of orthonormal basis functions and the small component using kinetically balanced basis functions.

Both methods were found to produce spurious energy states; however, the Variational Method resulted in fewer such states for a given number of basis functions (or spinors, in the case of the Basis Expansion Method). Despite this advantage, the Variational Method exhibited slower computational performance and a less rapid convergence of the largest positive energy eigenvalue to the theoretical ground-state energy compared to the Basis Expansion Method.

This project, undertaken in collaboration with Dr Andrea Rocco, seeks to investigate the mechanisms by which systems attain equilibrium when interacting with a Non-Markovian bath. Currently in its conceptualization phase, this research has not yet commenced but aims to provide foundational insights into the role of memory effects and non-Markovian dynamics in equilibrium processes.