2.1.3. Radiative Dissipation

The Lindblad-type radiative dissipation in (1), which shows the emission of the free photon into an external space, is given as the following equation,

$$\mathcal{L}^{(\mathbf{r})}\rho(t) = \frac{\gamma^{(\mathbf{r})}}{2} \sum\_{i,j} \left( 2a\_i \rho(t) a\_j^\dagger - \left\{ a\_i^\dagger a\_{j\prime} \rho(t) \right\} \right), \tag{5}$$

where *γ*(r) represents the relaxation constant via the free photon in an external space, and the curly brackets are the notation of the anti-commutation relation. It is worth noting the summation of nodes labeled by the indices *i* and *j*. The relaxation involves both allowed and forbidden transitions of the free photon depending the symmetry of the spatial distribution of the total dressed photon excitation.
