Large Deviations for Chiral Transition through Path Integral

An noise-induced mechanism has been revealed by some authors recently for the homochirality in a chiral system. Motivated by such stochastic process, we study the noise-induced transition in the system. The chiral transition, say the transition between chiral states, is impossible in the deterministic view if the homochirality has been converged, but is a rare event when noise is involved. We study the rare event by using the large deviation theory (LDT) and figure out the LDT rate functional for the transition probability through the Doi-Peliti second quantization path integral method. In order to check the correctness of our work, we have derived the Langevin equations through the path integral method by using the Hubbard-Stratonovich transformation, and recover the equations reported by other authors through a different method.