Non-Markovian dynamics of bottomonia in the QGP

The evolution of quarkonia in the QGP medium can be described through the formalism of open quantum systems (OQS). In previous works with OQS, the quarkonium evolution was studied by working in either quantum Brownian or optical regime. In this paper, we set up a general non-Markovian master equation to describe the evolution of the quarkonia in the medium. Because of the non-Markovian nature, it cannot be cast in Lindblad form, which makes it challenging to solve. We numerically solve the master equation for <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi mathvariant="normal">ϒ</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>1</a:mn> <a:mi>S</a:mi> <a:mo stretchy="false">)</a:mo> </a:mrow> </a:math> without considering stochastic jumps for Bjorken and viscous hydrodynamic background at energies relevant to the large hadron collider (LHC) and relativistic heavy ion collider (RHIC). We quantify the effect of the hierarchy between the system timescale, <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:msub> <f:mi>τ</f:mi> <f:mi mathvariant="normal">S</f:mi> </f:msub> <f:mo>∼</f:mo> <f:mn>1</f:mn> <f:mo>/</f:mo> <f:msub> <f:mi>E</f:mi> <f:mi>b</f:mi> </f:msub> </f:math> , and the environment timescale, <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msub> <i:mi>τ</i:mi> <i:mi mathvariant="normal">E</i:mi> </i:msub> </i:math> , on quarkonium evolution and show that it significantly affects the nuclear modification factor. A comparison of our results with the existing experimental data from the LHC and RHIC is presented.