Exact scattering eigenstates in double quantum-dot systems with an interdot Coulomb interaction
We study a double quantum-dot system which consists of two leads of noninteracting electrons and two quantum dots with an interdot Coulomb interaction. We assume spinless electrons and consider arbitrary complex values of all lead-dot couplings and an interdot coupling. We construct exact many-electron scattering eigenstates whose incident states are free-electronic plane waves in the leads. Due to the interaction, some of the incident plane waves are scattered to two-body and three-body bound states. The binding strength of the many-body bound states is affected by the arrangement of the two quantum dots, by which we observe an interplay of the Coulomb interaction and quantum interference. We can understand the many-body bound states in terms of many-body resonances.
In the footsteps of our previous work \cite{RamatonBoschi} we generalize the Stefan-Boltzmann and Wien's displacement laws for the $ \textrm{AdS}_5 \times {\cal S}^5 $ spacetime, the background of the AdS/CFT correspondence foremost realization. Our results take into account the $ \textrm{AdS}_5 \times {\cal S}^5 $ full dimensionality in the electromagnetic field $A^{\mu}$ wave equation, which yields the higher-dimensional blackbody characteristic features suggested in literature. In particular, the total radiated power and the spectral radiancy match the original Stefan-Boltzmann and Wien's displacement laws in the low-energy regime up to available experimental data.