  We propose an ab-initio molecular dynamics method, capable to reduce
dramatically the autocorrelation time required for the simulation of classical
and quantum particles at finite temperature. The method is based on an
efficient implementation of a first order
  Langevin dynamics modified by means of a suitable, position dependent
acceleration matrix $S$. Here we apply this technique, within a Quantum Monte
Carlo (QMC) based wavefuntion approach and within the Born-Oppheneimer
approximation, for determining the phase diagram of high-pressure Hydrogen with
simulations much longer than the autocorrelation time. With the proposed
method, we are able to equilibrate in few hundreds steps even close to the
liquid-liquid phase transition (LLT).
  Within our approach we find that the LLT transition is consistent with recent
density functionals predicting a much larger transition pressures when the long
range dispersive forces are taken into account.
