Abstract: We review the Hubbard model and its extensions as a framework to describe electron correlation and the Mott metal-insulator transition. Starting from the atomic and band limits, we explore the emergence of Hubbard sub-bands and the Mott transition through Hubbard-I decoupling. The strong-coupling expansion leads to the t-J model, highlighting spin-exchange mechanisms. We then study the extended Hubbard model with emphasis on orbital physics and transition metal oxides. The role of super-exchange, charge-transfer effects are discussed in relation to real materials. Finally, the Dynamical Mean Field Theory (DMFT) approach is introduced to capture certain features of the Hubbard model, including emergence of sub-bands, the evolution of spectral weight.
Abstract: This report introduces photonic topological insulators (PTIs), drawing parallels with electronic systems like the Integer and Quantum Spin Hall Effects. Key concepts include the Berry phase, Chern number, and bulk-edge correspondence. We explore the translation of topology to photonic systems, highlight experimental realizations, and discuss potential applications of PTIs.
Abstract: This report begins with discussing the evolution of open quantum systems and corresponding Quantum Master Equation (QME). The main emphasis is given to the Fluctuation Regulated Quantum Master Equation (FRQME) and its applications on the dynamics of driven dissipative two-level systems (TLS) and quantum optimal control of that TLS. I have also presented the results of numerical simulations for the solutions of the FRQME in the report.
Title:"Open Quantum Systems: Kraus Representation Theorem and Quantum Channels."
Contributors: Pritish Karmakar, Ravi
Inderpreet Singh and R. Pradeep.
Superviser: Prof. Sourin Das, Department of Physical Sciences, IISER
Kolkata.
Abstract: This paper
begins by discussing the general dynamics of an open system. We explore the theory of quantum measurements and elaborate on the intricacies of operator sum representation including the Kraus representation theorem. Finally, the main emphasis is given to the quantum channels including amplitude-damping, dephasing, bit-flip, phase-flip, and depolarizing channels.
Title:"On Polarization Properties of Light, Gaussian Beams and Spin-Orbit Interaction of Light."
Contributor: Pritish Karmakar.
Superviser: Prof. Ayan Banerjee, Department of Physical Sciences, IISER
Kolkata.
Abstract: I worked in
optics and polarization, delving into topics such as Jones and Stokes-Mueller formalism, Gaussian beam
properties, and light momentum principles. My work covered spin-orbit interaction dynamics, including
geometric phases and their manifestations, especially within anisotropic media.