MCAIM Graduate Seminar Seminar

The Hamiltonian, which is for many systems the energy function, plays an important role in both classical and quantum evolution of systems. Generally, it is a positive real-valued function in classical mechanics corresponding to a positive self-adjoint operator in quantum mechanics. But what happens if we allow it to be complex-valued (i.e., non-Hermitian in the quantum sense)? In this talk, we will explore some interesting geometric aspects of this question. In particular, we will give a quick overview of the Hamiltonian formulation of classical mechanics and how to get a quantum description using a quantization scheme. Then, we will describe the (classical) time evolution of a system under a complex Hamiltonian and finally, we will make a few remarks about what this tells us about quantum evolution.
Speaker(s): Reebhu Bhattacharyya (University of Michigan)