Recently, the strong friction limit for a quantum system coupled to a heat bath environment has been explored starting from the exact path integral formulation. Generalizing the classical Smoluchowski limit to low temperatures a time evolution equation for the position distribution, the quantum Smoluchowski equation, has been derived. This important result can even be extended to a quantum Fokker--Planck equation in full phase space. Here, we review these fundamental findings from a physical perspective and apply them to the Kramers barrier escape problem at low temperatures and strong friction.

PACS numbers: 03.65.Yz, 05.30.Ch, 73.23.--b, 82.20.--w