Renormalization Group Approach for Modified vdP Oscillator with PT\mathcal{PT} Symmetric Non-Hermitian Interaction

We consider a modified version of the well-known 2d vdP oscillator with a new non-Hermitian interaction. The usual perturbative approach fails to provide the classical dynamics of the system as the classical solutions become divergent in the long time limit. These kinds of divergences are similar to what occurs in quantum field theory and critical phenomena. The Renormalization Group (RG) technique for the dynamical system has been used to eliminate the divergences in the perturbative solution of the 2d vdP oscillator and to provide a physically acceptable solution which is shown to be consistent with numerical study. We further investigate the model in the framework of non-Hermitian quantum mechanics to show the $\mathcal{PT}$ phase transition in the system.Comment: 12 pages, Latex, 6 Fig

Proceedings of National Conference on Relevance of Engineering and Science for Environment and Society

This conference proceedings contains articles on the various research ideas of the academic community and practitioners presented at the National Conference on Relevance of Engineering and Science for Environment and Society (R{ES}2 2021). R{ES}2 2021 was organized by Shri Pandurang Pratishthan’s, Karmayogi Engineering College, Shelve, Pandharpur, India on July 25th, 2021. Conference Title: National Conference on Relevance of Engineering and Science for Environment and SocietyConference Acronym: R{ES}2 2021Conference Date: 25 July 2021Conference Location: Online (Virtual Mode)Conference Organizers: Shri Pandurang Pratishthan’s, Karmayogi Engineering College, Shelve, Pandharpur, India