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Explore the advanced theoretical framework of generalized hydrodynamics in this third lecture delivered by Benjamin Doyon at the International Centre for Theoretical Sciences. Delve into the sophisticated mathematical and physical principles that extend traditional hydrodynamic theory to quantum integrable systems and non-equilibrium statistical mechanics. Learn how generalized hydrodynamics provides a powerful tool for understanding transport phenomena in one-dimensional quantum many-body systems, particularly those with integrability constraints. Examine the theoretical foundations that bridge quantum mechanics and classical fluid dynamics, focusing on the emergence of ballistic transport and the role of quasiparticles in integrable models. Discover how this framework applies to experimental systems such as ultracold atomic gases and quantum spin chains, providing insights into non-equilibrium dynamics and thermalization processes. Master the mathematical techniques used to derive hydrodynamic equations from microscopic quantum models, including the treatment of local conservation laws and the construction of thermodynamic Bethe ansatz. Understand the connections between generalized hydrodynamics and other areas of theoretical physics, including conformal field theory and quantum field theory. This lecture forms part of the comprehensive Bangalore School on Statistical Physics-XVI, designed to bridge the gap between master's-level coursework and cutting-edge research in statistical physics for PhD students, postdoctoral researchers, and faculty members.
