Theoretical work has extended the original model to include the effects of dissipation and damping, typically via a phenomenological approach. Proposed extensions have also incorporated the inclusion of multiple modes of the quantum field, allowing for coupling to additional energy levels within the atom, or the presence of multiple atoms interacting with the same field. Some attempt has also been made to go beyond the so-called rotating-wave approximation that is usually employed (see the mathematical derivation below). The coupling of a single quantum field mode with multiple (formula_3) two-state subsystems (equivalent to spins higher than 1/2) is known as the Dicke model or the Tavis–Cummings model. For example, it applies to a high quality resonant cavity containing multiple identical atoms with transitions near the cavity resonance, or a resonator coupled to multiple quantum dots on a superconducting circuit. It reduces to the Jaynes–Cummings model for the case formula_4.