Abstract
A microscopic approach has been employed to study the kaon and $\Lambda$ productions in heavy ion collisions. The productions of $K^+$ and $\Lambda$ have been studied within the framework of Boltzmann transport equation for various beam energies. We find a non-monotonic horn like structure for $K^+/\pi^+$ and $\Lambda/\pi$ when plotted against centre of mass energies ($\sqrt s_{\mathrm NN}$) with the assumption of initial partonic phase for $\sqrt s_{\mathrm NN}$ beyond a certain threshold. However, the ratio $K^+/\pi^+$ shows a monotonic nature when a hadronic initial state is considered for all $\sqrt s_{\mathrm NN}$. Experimental values of $K^-/\pi^-$ for different $\sqrt{s_{\mathrm NN}}$ are also reproduced within the ambit of the same formalism.
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