class TrialComputeAdd : public feasst::TrialCompute

The derivation of the acceptance criteria follows a similar procedure as descibed in TrialComputeMove, except with the following differences.

The limiting distribution in the grand canonical ensemble is

$$\pi_i \propto \frac{e^{-\beta U + \beta \mu_t N_t}}{\Lambda^{dN}}$$

where $$\mu_t$$ is the chemical potential of particles of type t, $$\Lambda$$ is the de Broglie wavelength, $$N_t$$ is the number of particles of type t and d is the dimension.

The transition probabilities are as follows, assuming that this move is coupled with a trial that removes particles with the same selection weight.

 Forward event [reverse event] Probability, $$\pi_{on}$$ [reverse probability, $$\pi_{no}$$] Select insert trial [Select remove trial] $$1/w$$ $$[1/w]$$ Place particle of type t [Delete particle type t] $$1/V$$ $$\left[\frac{1}{N_t+1}\right]$$ Accept [Accept] $$min(1, \chi)$$ $$[min(1, 1/\chi)]$$

Application of local detailed balance yields the acceptance probability, $$\chi$$.

$$\frac{e^{-\beta U_o + \beta\mu_t N_t}}{\Lambda^{dN}w V }min(1, \chi) = \frac{e^{-\beta U_n + \beta\mu_t (N_t+1)}}{\Lambda^{d(N+1)}w (N_t+1)} min(1, 1/\chi)$$

$$\chi = \frac{V e^{-\beta\Delta U + \beta\mu_t}}{(N_t+1)\Lambda^d}$$

Note that the number of particles, $$N_t$$ is from the perspective of the old state. Thus, if the particle has already been added during computation of $$\chi$$, then $$N_t + 1 \rightarrow N_t$$. The same applies for TrialComputeRemove.

The de Broglie wavelength, $$\Lambda^d$$, is absorbed into the definition of $$\mu$$ for convenience, $$\mu + \ln(\Lambda^d)/\beta \rightarrow \mu$$.

Public Functions

void perturb_and_acceptance(Criteria *criteria, System *system, Acceptance *acceptance, std::vector<TrialStage*> *stages, Random *random)

Perform the Perturbations and determine acceptance.