We consider a quantum system coupled to a dissipative background with many
degrees of freedom using the Monte Carlo wave function method. Instead of d
ealing with a density matrix which can be very highly dimensional, the meth
od consists of integrating a stochastic Schrodinger equation with a non-Her
mitian damping term in the evolution operator, and with random quantum jump
s. The method is applied to the diffusion of hydrogen on the Ni(111) surfac
e below 100 K. We show that the recent experimental diffusion data for this
system can be understood through an interband activation process, followed
by quantum tunneling.