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Explore advanced concepts in thermal transport phenomena through the lens of differential geometry and quantum field theory anomalies in this comprehensive physics lecture. Delve into the intricate relationships between geometric structures and heat conduction in condensed matter systems, examining how topological properties and geometric constraints influence thermal transport coefficients. Investigate the role of quantum anomalies in thermal conductivity, learning how chiral and gravitational anomalies manifest in transport properties of materials with non-trivial band structures. Analyze theoretical frameworks that connect curvature effects, Berry phases, and anomalous transport phenomena, with particular emphasis on Weyl semimetals and other topological phases of matter. Study the mathematical formalism underlying anomalous thermal Hall effects and examine experimental signatures of geometric contributions to heat transport. Gain insights into cutting-edge research connecting quantum field theory concepts to practical condensed matter applications, including discussions of hydrodynamic approaches to anomalous transport and the interplay between electronic and phononic contributions to thermal conductivity in systems with broken time-reversal or inversion symmetry.
