  We introduce a type of quantum dissipation -- local quantum friction -- by
adding to the Hamiltonian a local potential that breaks time-reversal
invariance so as to cool the system. Unlike the Kossakowski-Lindblad master
equation, local quantum friction directly effects unitary evolution of the
wavefunctions rather than the density matrix: it may thus be used to cool
fermionic many-body systems with thousands of wavefunctions that must remain
orthogonal. In addition to providing an efficient way to simulate quantum
dissipation and non-equilibrium dynamics, local quantum friction coupled with
adiabatic state preparation significantly speeds up many-body simulations,
making the solution of the time-dependent Schr\"odinger equation significantly
simpler than the solution of its stationary counterpart.
