Dynamical fermionization in a one-dimensional Bose-Fermi mixture

After release from the trap momentum distribution of an impenetrable gas asymptotically approaches that a spinless noninteracting Fermi in initial trap. This phenomenon is called dynamical fermionization and, very recently, has been experimentally confirmed case Lieb-Liniger model Tonks-Girardeau regime. We prove analytically and confirm numerically following removal axial confinement strongly interacting Bose-Fermi mixture exhibits asymptotical each component same shape as its density profile at $t=0$. Under sudden change frequency to new nonzero value dynamics both fermionic bosonic distributions presents characteristics which are similar single bosons experiencing quench. Our results derived using product representation for correlation functions which, addition analytical considerations, can be implemented easily with complexity scales polynomially number particles.