  We study how fluxes on the domain wall world volume modify quantum fusion of
two distant parallel domain walls into a composite wall. The elementary wall
fluxes can be separated into parallel and antiparallel components. The parallel
component affects neither the binding energy nor the process of quantum merger.
The antiparallel fluxes, instead, increase the binding energy and, against
naive expectations, suppress quantum fusion. In the small flux limit we
explicitly find the bounce solution and the fusion rate as a function of the
flux. We argue that at large (antiparallel) fluxes there exists a critical
value of the flux (versus the difference in the wall tensions), which switches
off quantum fusion altogether. This phenomenon of flux-related wall
stabilization is rather peculiar: it is unrelated to any conserved quantity.
Our consideration of the flux-related all stabilization is based on
substantiated arguments that fall short of complete proof.
