How Quantum Is Bottomonium in the Quark-Gluon Plasma?

Abstract

We study how much quantum structure bottomonium retains during its evolution in the quark-gluon plasma. Within the open quantum system framework, we simulate the Lindblad equation obtained from potential nonrelativistic QCD in the quantum Brownian regime. From the resulting real-time evolution of the bottomonium density matrix, we compute the Wigner transform and study its negativity as a measure of nonclassicality and a test of a key condition underlying classical Langevin-type approximations. We find that the medium suppresses the negativity, which nevertheless approaches a finite plateau close to that of the $1\mathrm{S}$ state. The overlaps with the excited $2\mathrm{S}$ and $3\mathrm{S}$ states arise from near-canceling positive and negative phase-space contributions, driven by negative regions in the Wigner transforms of the bound-state projectors, while the $1\mathrm{S}$ overlap is insensitive to such contributions. We further show that the position-space coherence is similarly suppressed and plateaus close to the 1S value. We trace the finite residual quantum structure to conditional purification: the medium preferentially dissolves weakly bound and unbound modes with large $⟨r^2⟩$, driving the surviving singlet $\mathrm{S}$-wave ensemble toward the $1\mathrm{S}$ state. More broadly, these results reveal that classicalization is partial and observable dependent, a feature that is relevant across applications of open quantum system methods in fundamental physics.

Comments: 11 pages, 9 figures