Extended Dissipaton Theory with Application to Adatom-Graphene Composite

In this paper, we present the extended dissipaton theory, including the dissipaton-equation-of-motion formalism and the equivalent dissipaton-embedded quantum master equation. These are exact, non-Markovian, and nonperturbative theories, capable of handling not only linear but also quadratic environmental couplings. These scenarios are prevalent in a variety of strongly correlated electronic systems, including mesoscopic nanodevices and superconductors. As a demonstration, we apply the present theory to simulate the spectral functions of an adatom on a graphene substrate. We analyze the spectral peaks in the presence of the graphene substrate and compare them to those obtained in conventional metal environments. The adatom's spectral functions reveal intricate behaviors arising from the band structure of graphene.