Von Neumann entropy and Lindblad decoherence in the high-energy limit of strong interactions

Quantum properties of the state associated to the gluon Green's function in the Balitsky-Fadin-Kuraev-Lipatov approach are studied using a discretization in virtuality space. Considering the coupling constant as imaginary, its density matrix corresponds to a pure state for any energy. Nonlinear corrections due to high gluon densities are modeled through a suppression of infrared modes in the Hamiltonian making it no longer Hermitian. This introduces quantum decoherence into the evolution equation. When the coupling is real this leads to unbounded normalization of states which becomes bounded for sufficient saturation of infrared modes. Physical quantum properties, such as a purity smaller than one or a positive von Neumann entropy, hence are recovered when the infrared/ultraviolet original symmetry of the formalism is broken. Similarly to the work of Armesto, Domínguez, Kovner, Lublinsky and Skokov in [J. High Energy Phys. 05 (2019) 025], an evolution equation of Lindblad type for the normalized density matrix describing the open system is obtained.