Skyrmion formation in 1+1 dimensions with chemical potential

Formation of topological objects during phase transitions has been discussed extensively in literature. In all these discussions, defects and antidefects form with equal probabilities. In contrast, many physical situations, such as formation of baryons in relativistic heavy-ion collisions at present energies, flux tube formation in superconductors in the presence of external magnetic field, and formation of superfluid vortices in a rotating vessel, require a mechanism which can bias (say) defects over antidefects. Such a bias can crucially affect defect-antidefect correlations, apart from its effects on defect density. In this paper we initiate an investigation for the basic mechanism of biased formation of defects. For Skyrmions in 1 + 1 dimensions, we show that incorporation of a chemical potential term in the effective potential leads to a domain structure where order parameter is spatially varying. We show that this leads to biased formation of Skyrmions.