TrialPositionSwap

class TrialPositionSwap : public feasst::Trial

Attempt to change the identity of two particles of different types in the same configuration. This trial is only valid for rigid particles.

The limiting distribution in the canonical ensemble is given by

\(\frac{\Pi_{n}}{\Pi_{o}} = e^{-\beta\Delta (U_1+U_2)}\)

The transition probabilities are as follows.

Forward	\(\pi_{o \rightarrow n}\)
Choose particle of type i	\(1/N_{i}\)
Choose particle of type j	\(1/N_{j}\)
Exchange the types of the particles and rotate both of them	\(P_{\omega i n}\mathrm{d}\boldsymbol{\omega}\) \(P_{\omega j n}\mathrm{d}\boldsymbol{\omega}\)

Reverse	\(\pi_{n \rightarrow o}\)
Choose particle of type i	\(1/N_{i}\)
Choose particle of type j	\(1/N_{j}\)
Exchange the types of the particles and rotate both of them	\(P_{\omega i o}\mathrm{d}\boldsymbol{\omega}\) \(P_{\omega j o}\mathrm{d}\boldsymbol{\omega}\)

Application of local detailed balance yields the acceptance probability,

\(\chi = \frac{P_{\omega i o}P_{\omega j o}}{P_{\omega i n}P_{\omega j n}} e^{-\beta \Delta U}\)