Tunnel creation of kink-antikink pairs from an inhomogeneous vacuum by an external field

The problem of under-barrier creation of kink-antikink pairs by a constant background field is considered within the framework of the one-dimensional sine-Gordon and ${\mathrm{\phi }}^4$ models with an inserted periodic lattice of local defects, which renders the true vacuum of the models spatially inhomogeneous. Two types of defects are considered, viz., the ones generating the inhomogeneous vacuum containing dipoles or quadrupoles pinned at sites of the lattice. A specific feature of the pair production in such a system is that one or both members of the pair appear on the mass shell in a state pinned at a site. The energy of a pinned kink is lower than that of a free kink, which results in a substantially shorter under-barrier trajectory and, hence, gives rise to a strong growth of the pair-production rate. In the absence of the background field the dipole inhomogeneous vacuum is double degenerate in its polarization, which gives rise to kinks of the second kind—the ones reversing the polarization. Mass, charge, and an exponent determining the kink-antikink tunnel-creation rate are found for these kinks.