Joule heat in point contacts

We considered Joule heat in point contacts which are the elementary building blocks of ballistic devices with nonlocal transport based on two dimensional electron gas. We present a theory of a point contact up to second order in the applied voltage. Out of our calculation arises the main difference in Joule heat delivery between local and nonlocal transport. While for local transport the Joule heat is delivered in the same domains where the drop of potential happens, in the case of nonlocal transport these domains are well separated in space.