  We present an elementary and self-contained account of the analogies existing
between classical diffusion and the imaginary-time evolution of quantum
systems. These analogies are used to develop a new quantum simulation method
which allows to calculate the ground-state expectation values of local
observables without any mixed estimates nor population-control bias, as well as
static and dynamic (in imaginary time) response functions. This method, which
we name Reptation Quantum Monte Carlo, is demonstrated with a few case
applications to 4He, including the calculation of total and potential energies,
static and imaginary-time dependent density response functions, and low-lying
excitation energies. Finally, we discuss the relations of our technique with
other simulation schemes.
