Quantum Information 2021/2022

Collection Number C22016
Collection Date -
We will review the notion of entanglement in quantum mechanics form the point of view of information theory, and how to quantify it and distinguish it from classical correlations. We will derive Bell inequalities and discuss their importance, and how quantum information protocols can use entanglement as a resource. Then we will analyze measurement theory in quantum mechanics, the notion of generalized measurements and quantum channels and their importance in the processing and transmission of information. We will introduce the notions of quantum circuits and see some of the most famous algorithms in quantum information processing, as well as in quantum cryptography. We will also talk about the notion of distances and fidelity between states from the point of view of information theory and we will end with a little introduction to the notions of relativistic quantum information.

Geometry and Topology for Physicists 2021/2022

Collection Number C22017
Collection Date -
The aim of this course is to introduce concepts in topology and geometry for applications in theoretical physics. The topics will be chosen depending on time availability from the following list: topological manifolds and smooth manifolds, differential forms and integration on manifolds, Lie groups and Lie algebras, and Riemann surfaces, cohomology and the fundamental group.

Quantum Fields and Strings 2021/2022

Collection Number C22015
Collection Date -
This course covers three distinct topics: conformal field theory, anomalies, and string theory. The conformal field theory section of the course introduces conformal transformation and the conformal algebra, n-point functions in CFTs, and OPEs. The anomalies portion of the course focuses on the functional integral derivation of the chiral anomaly. The string theory part of the course derives the bosonic string spectrum and introduces T-duality and D-branes.

Classical and Quantum Chaos 2021/2022

Collection Number C22018
Collection Date -
Chaos, popularly known as the butterfly effect, is a ubiquitous phenomenon that renders a system's evolution unpredictable due to extreme sensitivity to initial conditions. Within the context of classical physics, it often occurs in nonintegrable Hamiltonian systems and is characterized by positive Lyapunov exponents. On the other hand, the notion of nonintegrability and chaos in quantum physics is still not well-understood and is an area of active research. Several signatures have been studied in the literature to identify quantum chaos but all of them fall short in some way or the other. In this course, we will first discuss the notions of classical integrability, and classical chaos and its characterization with Lyapunov exponents. Then, we will discuss a few well-studied signatures of quantum chaos and the subtleties associated with them.