Decoherence, the Hormander condition and subRiemannian geometry

Decoherence is an effect in quantum mechanics, it describes the suppression of interference effects due to the coupling to an environment. It is one of the main obstacles one has to overcome if one wants to make use of quantum effects, e.g., in quantum computers. 

In this talk I will describe how decoherence is related to the Hormander condition in the theory of PDE, which gives a condition for a second order PDE to be hypoelliptic, and explain the analogy between decoherence and hypoellpticity. The Hormander condition in turn is related to subRiemannian geometry, and it turns out that some notions from subRiemannian geometry can be of use in the study of decorence as well. 

In this talk I will give an introduction and overview of these notions and will not assume any background in decoherence, hypoellipticity or subRiemannian geometry.