Mathematics

The quantum adiabatic theorem is an important result in quantum mechanics. It states: A physical system remains in its instantaneous eigenstate if a given perturbation is acting on it slowly enough and if there is a gap between the eigenvalue and the rest of the Hamiltonian's spectrum.
In this talk I apply the concepts of the quantum adiabatic theorem to a similar adiabatic theorem for discrete and continuous time Markov chains. I find general bounds on the 'adiabatic time' with respect to the mixing time and I apply this bound to Ising models with Glauber dynamics on different dimensional tori.
Outside of some basic probability and analysis knowledge, this talk is self-contained.