My current interests are in hard condensed matter physics. My interest in theoretical condensed matter physics is related to how fundamental questions can arise with increasing complexity in systems and new laws and generalisations are required to explain them. Another aspect that has drawn me towards this field is the possibility of close collaboration with experimental groups. It is an integral part of the way I had envisioned myself as a researcher.
During my master's I worked on understanding the various ways the current flowing through a quantum dot or two quantum dots can be calculated. First, using the Keldysh formalism and the Meir-Wingreen formula and then using the rate equation formalism for when the coupling is weak.
- I implemented the Metropolis-Hastings algorithm to simulate the Ising model on a 2D lattice.
- I used it to study the dependence of hysterisis on various external parameters and replicate some of the results of 10.1103/PhysRevB.42.856
- I numerically solved the Allen-Cahn and Cahn-Hilliard equations using the Chebyshev spectral methods.
- Spectral methods usually have more accuracy compared to finite difference methods for small lattices. I was able to show the faster convergence and the 2D seperation of phases for the Allen-Cahn equation.
- The results for Cahn-Hilliard equation were however inconclusive. There was no significant increase in accuracy using Chebyshev Polynomials and this can perhaps be linked to the fourth derivative present in the equation.