JIMWLK Evolution, Lindblad Equation and Quantum-Classical Correspondence

Understand

In the Color Glass Condensate(CGC) effective theory, the physics of valence gluons with large longitudinal momentum is reflected in the distribution of color charges in the transverse plane.

• Averaging over the valence degrees of freedom is effected by integrating over classical color charges with some quasi probability weight functional $W[{\mathbf{j}}]$ whose evolution with rapidity is governed by the JIMWLK equation.
• In this paper, we reformulate this setup in terms of effective quantum field theory on valence Hilbert space governed by the reduced density matrix $\hat\rho$ for hard gluons, which is obtained after properly integrating out the soft gluon "environment".
• We show that the evolution of this density matrix with rapidity in the dense and dilute limits has the form of Lindblad equation.