by Prof. Kedar Damle, TIFR Mumbai

Abstract:

Solid state physicists try hard to reduce impurities and imperfections when making crystals of interesting materials. However, impurity effects are not always just a nuisance; sometimes they are at the heart of physics that is interesting in its own right, for example Anderson's famous discovery of electron wave localization and Broadbent and Hammersley's nearly contemporaneous identification of percolation transitions of a random medium. Manifestations of both phenomena remain of current interest in physics, and theoretical aspects remain of current interest at the intersection of probability theory, random geometry and computer science. In this talk, I will review this physics and then describe an interesting connection between a class of localization problems and an unusual percolation phenomenon. Apart from the motivation that comes from current research, the discussion will remain mostly at the level of undergraduate physics and mathematics/computer science (specifically, UG quantum and solid-state physics, and UG linear algebra and graph theory). [This story is based on Bhola & KD arxiv:2311.05634v2 (May2025); Bhola & KD, Phys. Rev. B 114, 105125 (2026); Ansari, Kundu, & KD Phys. Rev. B in press (arXiv:2602.24203); Ansari & KD, Phys. Rev. Lett. 132, 226504 (2024); KD, Phys. Rev. B 105, 235118 (2022); Bhola, Biswas, Islam, KD Phys. Rev. X 12, 021058 (2022); Sanyal, KD, Motrunich, Phys. Rev. Lett. 117, 116806 (2016).]