Single-particle approach to many-body relaxation dynamics

This paper addresses the challenge of modeling relaxation dynamics in quantum many -body systems, specifically focusing on electrons in graphene nanoflakes. While quantum many -body techniques effectively describe dynamics up to a few particles, these approaches become computationally intractable for large systems. Larger systems may be tackled with a single -particle approach that, however, struggles to incorporate relaxation effects. Existing relaxation models encounter issues such as an inability to capture system complexity and violation of the Pauli principle. In this paper, we propose a single -particle model that accounts for various relaxation effects at the crossroads of quantum optics and solid-state photonics, that overcomes the limitations of previous models. Our approach is rooted in the quantum -optical Lindblad model, where relaxation rates are deactivated once the target levels saturate due to the Pauli principle. This approach is referred to as the saturated -Lindblad model. To validate the predictions of the saturated -Lindblad model, we confront them against phenomenological and many -body physics models in low -dimensional systems, including atomic chains and graphene nanoflakes. Remarkably, the saturated -Lindblad model exhibits excellent agreement with few -body calculations, distinguishing itself from other existing approaches. Moreover, by assigning different relaxation rates to different transitions, we successfully reproduce cascade deexcitation dynamics and predict emission spectra. The saturated -Lindblad model offers the ability to describe dynamics in systems of practical sizes, encompassing a wide range of structures that can be effectively captured within the single -particle description.