Mathematical Sciences Department QIT Thinking Seminar: Harmony Zhan, WPI

Title: Does Laplacian quantum fractional revival occur on trees?

Abstract: A spin network exhibits fractional revival if a state localized at site u evolves to a superposition of states localized at site u and site v. We explore this phenomenon on trees, which, as minimally connected graphs, are natural candidates for physical realization. We show that relative to the Laplacian Hamiltonian, no tree on more than three vertices admits this phenomenon, except in the trivial case of periodicity. On the other hand, we can classify all paths and double stars that admit a relaxed version of this phenomenon called pretty good Laplacian fractional revival. This is joint work with Chan, Johnson, Liu, Schmidt, and Yin.