A study of the horn in the particle ratio $K^+/pi^+$ for central heavy-ion collisions as a function of the collision energy $sqrt{s}$ is presented. We analyse two different interpretations: the onset of deconfinement and the transition from a baryon- to a meson-dominated hadron gas. We use a realistic equation of state (EOS), which includes both hadron and quark degrees-of-freedom. The Taub-adiabate procedure is followed to determine the system at the early stage. Our results do not support an explanation of the horn as due to the onset of deconfinement. Using only hadronic EOS we reproduced the energy dependence of the $K^+/pi^+$ and $Lambda/pi^-$ ratios employing an experimental parametrisation of the freeze-out curve. We observe a transition between a baryon- and a meson-dominated regime; however, the reproduction of the $K^+/pi^+$ and $Lambda/pi^-$ ratios as a function of $sqrt{s}$ is not completely satisfying. We finally propose a new idea for the interpretation of the data, the roll-over scheme, in which the scalar meson field $sigma$ has not reached the thermal equilibrium at freeze-out. The rool-over scheme for the equilibration of the $sigma$-field is based on the inflation mechanism. The non-equilibrium evolution of the scalar field influences the particle production, e.g. $K^+/pi^+$, however, the fixing of the free parameters in this model is still an open issue.
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