External Projects
Gribov Ambiguity and Stochastic Quantization (Master's Thesis) [Aug 2023 - May 2024]
Supervisor: Prof. Laurent Baulieu, Sorbonne University, Paris & Dr. Vikash K. Ojha, SVNIT, Surat.
Abstract: The Gribov problem arises from the absence of a global section in the Yang-Mills fiber bundle due to the configuration space's non-trivial nature. We studied the Yang-Mills configuration space, particularly the Gribov and Fundamental Modular Regions, and the semi-classical implementation of path integral restriction to the Gribov Region. Additionally, we also explored Stochastic Quantization, an alternative c-number quantization formalism offering gauge fixing in Yang-Mills theory without the Gribov Problem.
Thesis
Certificate
Spanning Trees on a Lattice [Dec 2023 - Jan 2024]
Supervisor: Prof. Sourendu Gupta, TIFR, Mumbai.
Abstract: In a lattice gauge theory, for evaluating gauge variant observables, a class which many important observables belong to, it becomes necessary to fix the gauge. In this project, we demonstrate an explicit proof that imposing a spanning tree on the lattice maps the local gauge transformed copies to global gauge transformed copies. We also discuss theorems to count the number of spanning trees on a lattice, and provide algorithms to generate all of them. Further, we give a procedure to obtain the gauge transformation between two spanning trees. We also implement the above said algorithms in Mathematica, and discuss the computational challenges and possible improvements.
Report
Project
BFSS Model on the Lattice (DAAD-WISE project) [May 2023 - July 2023]
Supervisor: Dr. habil. Georg Bergner, Friedrich-Schiller-Universität Jena, Germany
Abstract: I contributed to the lattice implementation by writing Energy and 4-point correlator observables in the C++ implementation of the model, and further analyzing the simulation data to verify the model's behavior. We observed an anomalous behavior of gauge invariant 4-point correlators. To confirm the validity of the code, I wrote statistical analysis pipelines and tests for the simulation data, and also implemented the observable in the existing FORTRAN implementation and cross-verified the simulation results. Further, I also computed the Fermionic Energy on the lattice and verified that the temperature dependence matched with the approximate energy formula obtained by the supersymmetric Ward identities.
Report
Project
Particle Dark Matter: Existence And Constraints [May 2022 - Jul 2022]
Supervisor: Dr. Ranjan Laha, Center for High Energy Physics, Indian Institute of Science, Bangalore, India.
Abstract: We investigated the necessity of Dark Matter in Cosmological Models and examined the Evidence for the Existence and Properties of Particle Dark Matter from Cosmological Observations.
Report
Certificate
Lepton Oscillations (IASc, INSA, NASI - SRFP project) [Jun 2021 - Dec 2021]
Supervisor: Prof. Srubabati Goswami, Senior Professor, Physical Research Laboratory (PRL), Ahmedabad, India.
Abstract: We approached the question of why charged leptons do not oscillate, in connection to the flavor oscillations observed in the neutrinos. We understood that the mass squared difference and the uncertainty principle quantify the coherence distance of the flavor superpositions, which turn out to be very small for the charged leptons, thus ruling out the possibility of experimental observation of oscillations.
Report
Certificate
Statistical and Thermodynamic properties of Quark Gluon Plasma [Apr 2021 - Jun 2021]
Supervisor: Dr. Arvind Kumar, Dr B R Ambedkar National Institute of Technology, Jalandhar, India.
Abstract: I obtained a crude bound on the phase boundaries of the quark-gluon plasma via its statistical and thermodynamic properties while also addressing the question of the possibility of producing quark-gluon plasma in the laboratory.
Report
Institute Mini-Projects
Interacting Tachyonic Scalar Field as Dark Energy Candidate [Aug 2022 - Dec 2022]
Supervisor: Dr. Vikash K. Ojha, SVNIT, Surat.
Abstract: We modeled the dark energy as a Tachyonic Scalar Field that interacts with the matter content of the universe. I calculated the evolution of the various parameters, especially the functional form of scale factor and the Age of Universe. Notably, I obtained that the constraints on the coupling constant are the same as the case when the interaction term is different (Kundu, A. et.al ``Interacting tachyonic scalar field.'' Communications in Theoretical Physics 73.2 (2021): 025402.
ArXiv Preprint
Magnetic Monopoles [Jan 2022 - Apr 2022]
Supervisor: Dr. Vikash K. Ojha, SVNIT, Surat.
Abstract: We modeled a classically consistent two-potential formulation for classical electrodynamics with magnetic charged. I constructed the Lagrangian for a two-potential theory and derived Maxwell's equations with magnetic sources and Lorentz force equations for dyons were derived using Euler Lagrange equations.
Report
Dynamical Symmetries of the Kepler System [Aug 2021 - Dec 2021]
Supervisor: Prof. K N Pathak, SVNIT, Surat.
Abstract: We studied the SO(4) symmetry group of the Kepler system and its generators. I worked on the observation that the nontrivial symmetry operations that modify the eccentricity of the elliptic orbit keeping the energy constant translate to simple rotations in a 4D space with non-trivially reparameterized time.
Report
Independent Projects
Numerical Simulation of the Schwinger Model
Obtained, numerically, the real-time dynamics of particle density and entanglement entropies for the Schwinger model mapped to a spin-lattice model.[Reproduced the experimental results of
Muschik et al. (2023)]
To obtain the ground state of the Hamiltonian,
- Developed a variational quantum solver that implements the gradient descent, stochastic gradient, and ADAM method to obtain the separable product state best approximating the ground state.
- Developed and implemented a gradient descent algorithm for finding the Matrix Product State approximation of the ground state.
- Further employed quantum adiabatic evolution, and Physics Informed Neural Network to prepare the ground state.
Project
Physics Informed Neural Networks
Implemented Physics Informed Neural Networks (PINNs) for solving PDEs using both TensorFlow and PyTorch.
Used PINNs to first solve, as a benchmark, simple one variable differential equations, and then used it to solve the Heat Equation, Burgers Equation and Wave Equation in 2D. Further extended the methods to solve coupled differential equations.
Presently working on solving the Lotka-Volterra equations which, to verify if the equation invariants are preserved.
Project
CERN-ROOT
Practice MWEs from William Seligman's ROOT tutorial given at Nevis Labs.
Project
