First Passage Problems - Classical and Quantum - Lecture 3

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 in both classical stochastic processes and quantum mechanical systems. Learn about the fundamental differences between classical random walks and quantum walks, probability distributions of first passage times, and the role of quantum coherence in passage dynamics. Discover applications ranging from diffusion processes and reaction kinetics to quantum transport and measurement theory. Gain insights into analytical techniques for solving first passage problems, including generating functions, spectral methods, and path integral approaches. Understand the connections between first passage statistics and broader concepts in statistical physics such as survival probabilities, mean first passage times, and escape rates. This pedagogical presentation bridges the gap between master's-level statistical physics and current research frontiers, making complex theoretical concepts accessible to PhD students, postdoctoral researchers, and faculty members working in related fields.