arXiv subjects

Pragati Ashdhir

Publications and source records attributed to Pragati Ashdhir.

4 recordsLinked to original sources

arXiv2026

From Wave Scattering to Bloch Bands: A Time-Domain Approach to Band Formation in Periodic Media

Band formation in periodic media is a central topic in undergraduate solid-state physics, typically introduced through Bloch's theorem as an eigenvalue problem in reciprocal space for infinitely periodic systems. While mathematically elegant, this formulation can appear abstract: it assumes an idealized infinite lattice, shifts attention away from real-space wave dynamics, and presents band structures as static results rather than emergent consequences of wave propagation. Consequently, students often struggle to relate band gaps to familiar physical phenomena such as reflection, transmission, and interference, leading to a disconnect between formal band theory and observable wave behavior. We present a computational framework that addresses this gap by reconstructing band formation directly from time-domain wave propagation in finite periodic systems. Using a staggered-grid finite-difference time-domain scheme for elastic waves, a broadband excitation is propagated through a layered medium to obtain its transmission spectrum. From this, students extract the Bloch dispersion relation and observe spatial attenuation in band-gap regions, revealing the roles of multiple scattering and phase coherence. This approach provides a physically transparent pathway to band theory and enables exploration of finite-size effects, disorder, and defect-localized modes within a unified computational framework. Implemented through compact code and guided exercises, the method offers an accessible and versatile pedagogical tool, while also equipping students with transferable skills in numerical modeling of wave phenomena across disciplines.

physics.comp-ph↗

arXiv2026

From Fermat's Principle to Physics-Informed Neural Networks: A Unified Computational Approach to Variational Physics

Variational principles are a unifying mathematical framework across many areas of physics, yet their instruction at the undergraduate level remains primarily analytical. This work presents a pedagogically oriented and computationally enhanced approach to variational modeling that integrates contemporary tools including gradient descent, automatic differentiation, and Physics-Informed Neural Networks (PINNs). Classical variational problems are reformulated as optimization tasks and implemented using open-source Python libraries such as NumPy, Matplotlib, PyTorch, and JAX. The proposed approach is demonstrated through a progression of problems drawn from standard undergraduate curricula, including the derivation of Snell's law from Fermat's principle, projectile motion with and without viscous drag, simple harmonic motion, nonlinear pendulum with damping, steady-state heat conduction governed by the Laplace and Poisson equations with nonlinear temperature-dependent internal heat generation, the double pendulum via the principle of least action, and variational treatments of vibrating strings. In addition, quantum mechanical applications are presented through variational solutions of the hydrogen atom, helium atom, and a schematic nuclear model of the silicon nucleus, illustrating the breadth of the framework across classical, quantum, and nuclear physics. The approach aims to enhance conceptual understanding while simultaneously introducing students to modern computational research methodologies.

physics.comp-ph↗

arXiv2024

Rovibrational Spectroscopy of Diatomic Molecules in a Modified Morse Potential using Nikiforov-Uvarov Functional Analysis

The radial time-independent Schrödinger equation is solved for the diatomic molecules: H2, LiH, HCl, CO, VH, CrH, CuLi, TiC, NiC, and ScN using the recently developed Nikiforov-Uvarov Functional Analysis (NUFA) method. A modified Morse potential is considered and the Pekeris approximation is used to accommodate the centrifugal term. Accurate energy eigenvalues and eigenfunction solutions are obtained for vibrational ($\mathit{n}$) and rotational ($\ell$) states. For H2, LiH, HCl, and CO, excellent agreement is observed between present values and literature, provided that the Pekeris approximation remains valid. For other molecules, a collection of low and high-lying states not found in literature are reported. The NUFA method is a simple, general and accurate approach that may be applied to other interatomic potentials.

physics.chem-ph↗

arXiv2023

An exploration of the phonon frequency spectrum and Born-von Karman periodic boundary conditions in 1D and 2D Lattice systems using a computational approach

The concept of periodic boundary conditions (PBCs) is immensely significant in treating an ideal lattice of infinite extent as a finite lattice. An explicit usage of PBCs is often found missing in undergraduate texts on analytical treatment of lattice dynamics. The aim of the present work is to cover this gap by illustrating the application of Born-von Karman PBCs in lattice dynamical calculations using a computational approach. The equations of motion are set up for a linear diatomic lattice with a basis, using the nearest neighbour approximation. The solution is obtained by implementing fourth order Runge-Kutta algorithm in python. Fast Fourier Transform (FFT) technique is then used to obtain the phonon frequency spectrum corresponding to the computed solutions. Similar computations are extended to obtain the phonon spectrum for monatomic square and honeycomb lattices under the second nearest neighbour approximation. The computed results are validated against the analytical ones in each case. The target group of the present work are the students and educators at the undergraduate level.

physics.ed-ph↗