Chapter 115 Effect of Initial Fluctuations on Quarkonia Suppression Partha Bagchi, Nirupam Dutta and Ajit M. Srivastava Introduction Intensive investigation is going on in the field of quarkonia suppression in relativistic heavy-ion collisions. Matsui and Satz [1] first proposed J /ψ (bound state of charm and anti-charm) suppression as a signal for Quark Gluon Plasma (QGP) formation in Heavy Ion Collisions (HIC). The basic picture of this suppression is that due to the presence of deconfined medium, potential between quark (q ) and anti-quark ( ¯ q ) gets Debye screened. As a result the bound state swells in its size. If the Debye screening length of the medium is less than the radius of the state, then q ¯ q may not form bound state, leading to melting of the initial state. Due to this melting, the yield of the initial quarkonia state will be suppressed. Experimentally the phenomena was observed at CERN NA50 Experiment [2]. And J /ψ suppression pattern measured in Pb-Pb collisions at the CERN-SPS was used as evidence for deconfinement of quarks and gluons. However, there are other factors too that can lead to the suppression of J /ψ because of which it has not been possible to use J /ψ suppression as a clean signal for QGP. The above picture of evolution of quarkonia in medium is taken as either static picture or adiabatic evolution of quantum states under Time-dependent perturbation. That means the quarkonia evolves as a quantum states corresponding to a Hamiltonian which slowly changes with time. But the reality for HIC is far away from this scenario. The fireball produced in HIC evolves rapidly. Starting from the time of collision it takes only few fm time for hadronisation. That means if quarkonia is described in potential model then q ¯ q potential is no-doubt time dependent. It has been shown that P. Bagchi (B) · N. Dutta Variable Energy Cyclotron Centre, Kolkata, India e-mail: p.bagchi@vecc.gov.in N. Dutta e-mail: niripamdu@gmail.com A. M. Srivastava Institute of Physics, Bhubaneswar, India e-mail: ajit@iopb.res.in © Springer International Publishing AG, part of Springer Nature 2018 Md. Naimuddin (ed.), XXII DAE High Energy Physics Symposium, Springer Proceedings in Physics 203, https://doi.org/10.1007/978-3-319-73171-1_115 493