  We propose a simulation strategy which uses a classical device of linearly
coupled chain of springs to simulate quantum dynamics, in particular the
quantum walks. Through this strategy, we obtain the quantum wave function from
classical evolution. Specially, this goal is achieved with the classical
momenta of the particles on the chain and their Hilbert transform, from which
we construct the many-body momentum and Hilbert transformed momentum pair
correlation functions yielding the real and imaginary parts of the wave
function, respectively. With such wave function, we show that the classical
chain's energy and heat spreading densities can be related to the wave
function's modulus square. This relation indicates a concept of "phonon random
walks", and thus it provides a new perspective to understand ballistic heat
transport. The results here may give a definite answer to Feynman's idea of
using a classical device to simulate quantum physics.
