Quantum steady state processes far from equilibrium can be characterized by wave functions whose coefficients (in a fixed basis) evolve onto a fractal set. This is explicitly shown for the prototypical situation of heat flow from hot to cold reservoirs, with two spin-½ particles in a thermal gradient. The resulting dimensional loss, induced by the nonequilibrium environment, is related to the quantum transport process.

• Received 17 May 1994

DOI:https://doi.org/10.1103/PhysRevLett.74.246