In classical MC, the particles are represented by points in dimensional space, which are moved in every MC step. Most simply, one can choose the displacement of particles according to a uniform distribution. In PIMC, particles are represented by path and the equivalent moves would shift the entire polymer to a new position without changing its internal structure. We call this displacement moves and use them for the protons because their paths stay very localized. They are more efficient than single or multi-slice moves discussed in the following.
In a single slice move, one selects a particle and a time slice
and samples a new configuration while keeping and
fixed. From now on, the subscript denotes the time
slice. The optimal choice for the sampling distribution of is
given by the heat bath rule, which will be described in section
2.5.4. It states that
the new coordinate should by chosen according to its equilibrium