https://ar.iub.edu.bd/handle/11348/501 Thu, 10 Sep 2026 14:44:55 GMT 2026-09-10T14:44:55Z https://ar.iub.edu.bd/handle/11348/1544 Application of the bootstrap method for solving simple quantum mechanical systems: a study of effectiveness Del, Mollika Rani This thesis evaluates the effectiveness of the quantum mechanical bootstrap by applying it to two fundamental systems with known analytical solutions: the simple harmonic oscillator and the hydrogen atom. The bootstrap method is a consistency-based approach for determining the energy spectra of quantum mechanical systems without explicitly solving the Schrödinger equation. The methodology involves deriving moment recursion relations from the Hamiltonian and canonical commutation relations, then constructing Hankel matrices from these moments. Physical energy eigenvalues are identified by imposing positivity constraints—requiring that these matrices be positive semi-definite, which ensures the moments correspond to a valid quantum state. Trial energies that violate this condition are systematically excluded, and the allowed regions converge toward the true spectrum as the matrix size increases. Our results demonstrate that the bootstrap method successfully reproduces the known energy spectra for both systems. The findings confirm that the bootstrap provides a reliable alternative approach for spectral determination in quantum mechanics, suggesting its potential applicability to more complex systems where analytical solutions are unavailable. This thesis is submitted in partial fulfilment of the requirements for the degree of Bachelor of Science in Physics, 2026 Mon, 01 Jun 2026 00:00:00 GMT https://ar.iub.edu.bd/handle/11348/1544 2026-06-01T00:00:00Z https://ar.iub.edu.bd/handle/11348/1165 Theoretical Analysis of Electromagnetic Modes in Stratified Media Islam, Md. Ariful Electromagnetic wave propagation in stratified conducting media is a fundamental problem in underwater wireless communication and geophysical exploration. However, the accurate modeling of such environments is computationally challenging due to the highly oscillatory nature of the Bessel functions within the Sommerfeld integrals. This thesis develops a numerical method for analyzing electromagnetic modes in a three- layer model consisting of air, seawater, and seabed. The Global Matrix Method (GMM) is employed to formulate the boundary value problem, allowing for the rigorous treatment of multiple reflections at the interfaces. To resolve the numerical instability associated with the Sommerfeld integrals, a cus- tom integration solver was developed utilizing Romberg integration accelerated by the Shanks transformation (Wynn’s ε-algorithm)[1]. This hybrid approach ensures sta- ble convergence for the oscillatory integrands, overcoming the limitations of standard quadrature methods. Using this solver, the electromagnetic field components generated by a submerged Horizontal Magnetic Dipole (HMD) were explicitly calculated. The results confirm the transition from direct wave dominance in the near-field to lateral wave propaga- tion in the far-field, demonstrating the efficacy of the proposed method for modeling propagation in lossy stratified environments. Thu, 26 Feb 2026 00:00:00 GMT https://ar.iub.edu.bd/handle/11348/1165 2026-02-26T00:00:00Z https://ar.iub.edu.bd/handle/11348/1164 Page Curve Like Entanglement Dynamics in Many-Body Quantum Systems: A Study of a Free Fermionic Model Bhakta, Prosanto This thesis investigates entanglement dynamics in open quantum many-body systems, focusing on a one-dimensional free-fermion model in which a finite system is coupled to a large environment. We study the model introduced in Ref. [1], which becomes exactly solvable in the weak-coupling limit. Using resonant-level-model factorization, we derive analytical expressions for the entanglement dynamics and validate them with numerical simulations based on the correlation matrix formalism. We show that the system exhibits Page-curve-like behavior: the entanglement entropy grows at early times, reaches a maximum at the Page time (proportional to system size), and then decreases at late times. In the appropriate scaling regime, data for different system sizes collapse onto a single curve when plotted against the emitted-particle fraction. These results provide an analytically controlled and numerically validated framework for understanding Page-curve dynamics in open free-fermion systems. Sun, 01 Feb 2026 00:00:00 GMT https://ar.iub.edu.bd/handle/11348/1164 2026-02-01T00:00:00Z https://ar.iub.edu.bd/handle/11348/1000 The LHCb Detector and Testing and Performance Evaluation of AdePT in Gaussino Gomes, James Peter To meet the increasing computational demands of LHC experiments, this study explores the potential of GPU acceleration for electromagnetic simulations. The AdePT proto- type is integrated into the Gaussino framework and compared to the standard GEANT4. Initial results show that AdePT, while requiring optimization, demonstrates promising performance gains, especially with larger workloads. The successful simulation of elec- trons using AdePT highlights its potential for accelerating LHCb simulations and contributing to future physics analysis. Furthermore, a brief review of the LHCb detector is provided, encompassing its key subdetectors: the Vertex Locator (VELO), the tracking system (including the Trigger Tracker, Inner Tracker, and Outer Tracker), the Ring Imaging Cherenkov (RICH) detectors, the electromagnetic and hadronic calorimeters (ECAL and HCAL), and the muon system. Sat, 01 Feb 2025 00:00:00 GMT https://ar.iub.edu.bd/handle/11348/1000 2025-02-01T00:00:00Z