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Emphasizing the possibility of moderate suppression of heavy quarkoniumstates, we invite some attention towards the issue of real time evolution ofquarkonia during the cooling phase of quark gluon plasma(QGP). In this context,we have used time dependent perturbation theory to show that $\Upsilon(1S)$,$\Upsilon(2S)$, $J/\Psi$ can further be dissociated in the medium at atemperature below their dissociation thresholds even though they survive theDebye screening. We have presented and compared the dissociation probabilitiesand dissociation rates of these states in real and complex valued potential inthis article. We realise that our method is an approximate way to analyse theshort time behaviour of quarkonium in real valued potential and for long timebehaviour one must adopt a non perturbative technique for solving schr\"odingerequation of quarkonium bound states in evolving QGP. On the other hand theperturbation technique seems to be valid enough to deal with the same for acomplex valued quark anti-quark potential.

Bound to unbound states transitions of heavy quarkonia in the cooling phase of QGP