Quantum vs semiclassical description of in-QGP quarkonia in the quantum Brownian regime

In this work, we explore the range of validity of the semiclassical approximation of a quantum master equation designed to describe the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>c</a:mi> <a:mover accent="true"> <a:mi>c</a:mi> <a:mo stretchy="false">¯</a:mo> </a:mover> </a:math> dynamics in a quark-gluon plasma at various temperatures, in the quantum Brownian regime. We perform a comparative study of various properties, e.g., the charmonia yield, of the Wigner density obtained both with the Lindblad equation and with the associated semiclassical Fokker-Planck equation. The semiclassical description is found to reproduce with a remarkable accuracy the results obtained through the full quantum description. We show that, to a large extent, this can be attributed to the nonunitary components of the dynamics that result from the contact of the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>c</e:mi> <e:mover accent="true"> <e:mi>c</e:mi> <e:mo stretchy="false">¯</e:mo> </e:mover> </e:math> subsystem with the thermal quark-gluon bath, leading to a rapid classicalization of the subsystem.