NumImage approximation

From PIMC++

For a free particle, the value of the density matrix can be shown to be where is the distance between two particles at adjacent slices. In a periodic box, this is no longer the case. Instead, the density matrix should be periodic i.e where the index is the sum over all the periodic boxes. In the situation where the box length the former approximation is a good one. When this is not the case, then the kinetic density matrix will be incorrect and you will get wrong answers.

To remove this issue, there is a NumImage (Section: Actions) variable in the input. By setting this variable to 1, it will sum over the images in the nearest neighbor boxes (all 26 of them). Of course, doing so significantly slows down the calculation of the kinetic action in the code and should only be used when you are doing a calculation where it is critical. To see this effect in action, start making the free particle box iteratively smaller and compare against the analytical answer of a free particle in box. Eventually you will find a disagreement. Then increase NumImages and see the disagreement vanish. Complete this exercise by lowering the temperature (increasing ) so that the system is confined to its ground state.