Emergence of fluctuating traveling front solutions in macroscopic theory of noisy invasion fronts

摘要

The position of an invasion front, propagating into an unstable state, fluctuates because of the shot noisencoming from the discreteness of reacting particles and stochastic character of the reactions and diffusion. Anrecent macroscopic theory [Meerson and Sasorov, Phys. Rev. E 84, 030101(R) (2011)] yields the probability ofnobserving, during a long time, an unusually slow front. The theory is formulated as an effective Hamiltoniannmechanics which operates with the density field and the conjugate “momentum” field. Further, the theory assumesnthat the most probable density field history of an unusually slow front represents, up to small corrections, antraveling front solution of the Hamilton equations. Here we verify this assumption by solving the Hamiltonnequations numerically for models belonging to the directed percolation universality class.