"The Color Glass Condensate density matrix: Lindblad evolution, entanglement entropy and Wigner functional"

Presented by Alex Kovner, U Connecticut

Friday, April 5, 2019, 2:00 pm — Building 510, CFNS Seminar Room 2-38

We introduce the notion of the Color Glass Condensate (CGC)
density matrix ρ̂ . This generalizes the concept of probability
density for the distribution of the color charges in the hadronic wave
function and is consistent with understanding the CGC as an effective
theory after integration of part of the hadronic degrees of freedom. We
derive the evolution equations for the density matrix and show that it
has the celebrated Kossakowsky-Lindblad form describing the non-unitary
evolution of the density matrix of an open system. Additionally, we
consider the dilute limit and demonstrate that, at large rapidity, the
entanglement entropy of the density matrix grows linearly with rapidity
according to dSe/dy=γ, where γ is the leading BFKL eigenvalue.
We also discuss the evolution of ρ̂ in the saturated regime and
relate it to the Levin-Tuchin law and find that the entropy again grows
linearly with rapidity, but at a slower rate. Finally we introduce the
Wigner functional derived from this density matrix and discuss how it can
be used to determine the distribution of color currents, which may be
instrumental in understanding dynamical features of QCD at high energy.