1-dimensional hard rods
Hard Rods, 1-dimensional system with hard sphere interactions.
The statistical mechanics of this system can be solved exactly (see Ref. 1).
Canonical Ensemble: Configuration Integral
Consider a system of length defined in the range .
Our aim is to compute the partition function of a system of hard rods of length .
- External Potential; the whole length of the rod must be inside the range:
- Pair Potential:
where is the position of the center of the k-th rod.
Consider that the particles are ordered according to their label: ;
taking into account the pair potential we can write the canonical parttion function (configuration integral) of a system of particles as:
Variable change: ; we get: