TY - JOUR

T1 - The Color Glass Condensate density matrix

T2 - Lindblad evolution, entanglement entropy and Wigner functional

AU - Armesto, Néstor

AU - Domínguez, Fabio

AU - Kovner, Alex

AU - Lublinsky, Michael

AU - Skokov, Vladimir V.

N1 - Funding Information:
Article funded by SCOAP3.
Funding Information:
NA thanks Carlos Pajares for discussions on this subject. NA and FD were was supported by Ministerio de Ciencia e Innovación of Spain under project FPA2017-83814-P and Unidad de Excelencia María de Maetzu under project MDM-2016-0692, by Xunta de Galicia (Con-sellería de Educación) within the Strategic Unit AGRUP2015/11, and by FEDER. AK was
Publisher Copyright:
© 2019, The Author(s).

PY - 2019/5/1

Y1 - 2019/5/1

N2 - We introduce the notion of the Color Glass Condensate (CGC) density matrix ρ^. 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 the JIMWLK evolution equation arises here as the evolution of diagonal matrix elements of ρ in the color charge density basis. We analyze the behavior of this density matrix under high energy evolution and show that its purity decreases with energy. We show that the evolution equation for the density matrix 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 ddySe=γ, where γ is the leading BFKL eigenvalue. We also discuss the evolution of ρ^ 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. By analyzing the dense and dilute regimes of the full density matrix we are able to establish a duality between the regimes. 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.

AB - We introduce the notion of the Color Glass Condensate (CGC) density matrix ρ^. 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 the JIMWLK evolution equation arises here as the evolution of diagonal matrix elements of ρ in the color charge density basis. We analyze the behavior of this density matrix under high energy evolution and show that its purity decreases with energy. We show that the evolution equation for the density matrix 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 ddySe=γ, where γ is the leading BFKL eigenvalue. We also discuss the evolution of ρ^ 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. By analyzing the dense and dilute regimes of the full density matrix we are able to establish a duality between the regimes. 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.

KW - Heavy Ion Phenomenology

UR - http://www.scopus.com/inward/record.url?scp=85065472885&partnerID=8YFLogxK

U2 - 10.1007/JHEP05(2019)025

DO - 10.1007/JHEP05(2019)025

M3 - Article

AN - SCOPUS:85065472885

SN - 1126-6708

VL - 2019

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 5

M1 - 25

ER -