Projects

1. Is the Cosmos Transparent?

This was my 3rd year research project in cosmology carried out during my undergrad. It had theoretical and computational elements. The first half of the project was concerned with background reading on cosmology, Friedmann equations, cosmological models, distances, etc. In the second half, using the knowledge gained, I analysed supernovae (Union 2.1 compilation) and Hubble parameter data to constrain the transparency of the universe, and also worked out the constituent percentages of a flat, matter and cosmological constant dominated universe (ΛCDM cosmology). Cosmic transparency was constrained by considering how distances would be affected in a theoretically non-transparent universe. Comparing the theoretical predictions for distances and Hubble parameter against the observed data allowed me to put constraints on the transparency of the universe.

Quantifying Cosmic Transparency Project Report

2. Elegance of Phase Space

This was an independent mini-project I worked on during my undergrad. I was extremely intrigued by phase space trajectories when I studied Hamiltonian dynamics. Having seen a few phase diagrams in the lecture notes, I decided to code and plot phase space trajectories for some simple, 1 degree of freedom systems using Python. I first wrote down the hamiltonian for each system and then obtained the equations of motion analytically using Hamilton's equations. Once I had the equations of motion for each system, I wrote down a program to plot the corresponding phase space plot which showed different trajectories the system could take in phase space depending on total energy of the system.

Plotting Phase Space Project Report

3. Exploring Quantum Peculiarities

This was a summer internship I got during my 2nd year of undergrad in which I performed various quantum optics experiments with single photons at Physlab's Single Photon Quantum Mechanics and Quantum Information Lab. It had theoretical, experimental, and computational elements. In the first part of the project, I proved the utility of Type-1 spontaneous parametric down-conversion (SPDC) as a viable source of single photons. Using Type-1 SPDC as the source for single photons, I then conducted various nonlocality tests with experimentally-generated quantum states, studying quantum entanglement. In the later part of the project, I performed quantum state tomography for various two-qubit states by virtue of the density matrix formalism. The internship lasted around 2 months. Towards the end of the internship, I also studied the basics of quantum cryptography and the BB84 protocol. I emulated the BB84 protocol in a Jupyter notebook using Python.

Exploring Quantum Peculiarities Project Report

4. The N-body Problem

This was a purely computational project I undertook as part of the Scientific Computing module in my 3rd year of undergrad. I solved the 2-body and 3-body problem numerically by integrating the equations of motion in Python. Using the programs written, I proved Kepler's 1st law which states that orbits around the sun are conic sections, studied perturbations in moon's orbit in the Sun-Earth-Moon system, simulated the solar system, solved and simulated Burrau's problem, reproduced some periodic solutions to the 3-body problem from this paper and plotted equi-potential contours for a restricted 3-body system using which I studied Lagrange points. I also animated various solutions of the 3-body problem some of which can be seen below. This was a 4 week long project and everything, including the animation, was done in Python.

5. Geodesics and Horizons in Black Hole Spacetimes

This short project was carried out for the module "Modern Computational Techniques for Theoretical Physicists" offered in the Theoretical Physics MSc at King's College London. The work was done in three weeks during the term. In this project we carry out a brief study of some of the properties of the Schwarzschild black hole using Mathematica, mainly following Poisson's text "A Relativist's Toolkit: The Mathematics of Black-Hole Mechanics". A general relativity toolkit is built from scratch which computes the inverse metric, Christoffel symbols, Riemann tensor, etc. This toolkit is implemented to compute quantities of interest in Schwarzschild geometry. We show that the singularity at r=2M for the Schwarzschild spacetime is just a coordinate singularity using the Kretschmann scalar. We then plot light ray geodesics for four Schwarzschild black holes of varying mass and size using which we observe light ray bending due to the spacetime curvature of the black hole. In the last part of the study we prove that the event horizon of a Schwarzschild black hole is a null hypersurface, and obtain the expression for the surface gravity of a Schwarzschild black hole and confirm that it matches the result given in the literature.

Geodesics and Horizons in Black Hole Spacetimes Project Report

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