IMSc Theses/ Dissertations https://dspace.imsc.res.in/xmlui/handle/123456789/1 2026-10-05T01:18:59Z 2026-10-05T01:18:59Z Ravi Shanker https://dspace.imsc.res.in/xmlui/handle/123456789/933 2026-09-25T09:28:20Z 2026-01-01T00:00:00Z

Dirac eigenspectrum and the fate of anomalous U(1) chiral symmetry in thermal QCD [HBNI Th290]  Ravi Shanker This thesis presents a systematic investigation into the thermal phases and properties of strongly interacting nuclear matter described by Quantum Chromodynamics (QCD), focusing on the effective restoration of the different subgroups of the almost exact two-flavor chiral symmetry. From the properties of the eigenvalue spectrum of the quark Dirac operator calculated using lattice techniques, this thesis addresses the specific implications of the effective restoration, specifically of the anomalous singlet subgroup of chiral symmetry. Understanding the fate of chiral symmetry in QCD is of fundamental importance since its breaking is responsible for the origin of more than 99% of the mass of the visible universe.

2026-01-01T00:00:00Z Prem Kumar https://dspace.imsc.res.in/xmlui/handle/123456789/932 2026-09-25T09:29:43Z 2026-01-01T00:00:00Z

Open Quantum System: Dynamics and equilibrium state in weak and ultrastrong coupling limits [HBNI Th289]  Prem Kumar The spin-boson model is a widely used model for understanding the properties of a two level open quantum system. Accurately describing its dynamics often requires going beyond the weak system-environment coupling approximation. This work presents the analytical derivation of the complete fourth-order time-convolutionless (TCL) generator for a generic spin-boson model, accurate up to 4th order in the system-environment coupling parameter, for a very general class of environmental spectral densities. We use a higher-order quantum master equation (in system environment coupling strength) to analytically calculate all the deviations of the steady state of the quantum system up to second order in the coupling strength. We also show that this steady state is exactly identical to the corresponding generalized Gibbs state, the so-called quantum mean force Gibbs state, at arbitrary temperature. In the case of a semiconductor double-quantum-dot system, our results reveal corrections to the dynamics that may become physically significant in some parameter regimes. Furthermore, we report that the widely used second-order TCL master equation tends to overestimate the non Markovianity of a dynamics over a large parameter regime. The accuracy of the fourth order TCL generator is rigorously bench marked against specialized analytical calculations done for the Ohmic spectral density with Drude cutoff and against the numerically exact Hierarchical Equations of Motion technique.

2026-01-01T00:00:00Z Saurav Goyal https://dspace.imsc.res.in/xmlui/handle/123456789/931 2026-09-28T05:20:48Z 2026-01-01T00:00:00Z

Precision QCD Studies of Semi-Inclusive Deep Inelastic Scattering at Electron-Ion Collider [HBNI Th291] Saurav Goyal

2026-01-01T00:00:00Z Sushant https://dspace.imsc.res.in/xmlui/handle/123456789/930 2026-09-28T04:22:48Z 2026-01-01T00:00:00Z

Lower bound on height functions [HBNI Th288]  Sushant In this thesis, we investigate lower bounds for heights in connection with Lehmer’s conjecture, establishing new relationships between the Weil height and analytic objects such as the zeros of the Dedekind zeta function. Our results yield a novel criterion for Lehmer’s conjecture under the Generalized Riemann Hypothesis. In addition, we prove a p-adic equidistribution theorem for algebraic numbers of small Weil height, thereby verifying Lehmer’s conjecture for a broad class of algebraic numbers.

2026-01-01T00:00:00Z