Dynamics and Control of Oscillators and Spins Interacting with their Environment

Anthony Bloch, Department of Mathematics, University of Michigan

In this talk I will discuss various settings for oscillator and spin dynamics and control. I will consider both classical and quantum dynamics and the passage from reversible to irreversible behavior. I will describe oscillators coupled to heat baths with various kinds of coupling and the radiation induced instability of gyroscopically stable oscillators in the presence of these different couplings. In addition I will discuss oscillator and spin squeezing via pulses and the effects of a heat bath on the squeezed states. I will also consider infinite limits of finite-dimensional oscillator-heat bath systems and the role of Landau damping. Finally I will describe control theoretic aspects of Eberly Law model of coupled spin harmonic oscillator systems.