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Explore advanced concepts in first passage problems spanning both classical and quantum domains in this lecture from the Bangalore School on Statistical Physics-XVI. Delve into the mathematical frameworks and physical principles governing first passage phenomena, examining how particles or systems reach specific states or boundaries for the first time. Learn about the fundamental differences between classical random walks and quantum mechanical processes in first passage scenarios, including the role of quantum coherence and interference effects. Discover applications across diverse fields from condensed matter physics to biological systems, while understanding the computational methods used to solve first passage problems. Examine specific examples and case studies that illustrate the transition from classical to quantum behavior, and gain insights into current research frontiers where first passage problems play crucial roles in understanding transport phenomena, reaction kinetics, and quantum dynamics.
