Skyrm ion form ation in 1 + 1 dim ensions w ith chem icalpotential

Form ation oftopologicalobjects during phase transitions has been discussed extensively in literature. In allthese discussions defects and antidefectsform with equalprobabilities. In contrast,m any physicalsituations, such as form ation of baryons in relativistic heavy-ion collisions at present energies, ux tube form ation in superconductorsin the presence ofexternal m agnetic eld,and form ation ofsuper uid vortices in a rotating vessel,requirea m echanism which can bias(say)defectsoveranti-defects.Such a bias can crucially a ect defect-anti-defect correlations,apart from its e ects on defectdensity. In thispaperwe initiate an investigation forthe basic m echanism ofbiased form ation ofdefects. For Skyrm ionsin 1+ 1 dim ensions,we show thatincorporation ofa chem icalpotentialterm in thee ectivepotential leadsto a dom ain structure where orderparam eterisspatially varying. W e show thatthisleadsto biased form ation ofSkyrm ions. e-m ail:sunil@ iopb.res.in e-m ail:layek@ iopb.res.in e-m ail:ajit@ iopb.res.in e-m ail:ssanyal@ indiana.edu e-m ail:vivek krt@ hotm ail.com