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We investigate the thermoelectric properties of a T-shaped double quantum dot system described by a generalized Anderson Hamiltonian. The system's electrical conduction (G) and the fundamental thermoelectric parameters such as the Seebeck coefficient (S) and the thermal conductivity (κ), along with the system's thermoelectric figure of merit (ZT) are numerically estimated based on a Green's function formalism that includes contributions up to the Hartree-Fock level. Our results account for finite onsite Coulomb interaction terms in both component quantum dots and discuss various ways leading to an enhanced thermoelectric figure of merit for the system. We demonstrate that the presence of Fano resonances in the Coulomb blockade regime is responsible for a strong violation of the Wiedemann-Franz law and a considerable enhancement of the system's figure of merit (ZT ).

We study the d -dimensional Bose gas at finite temperature using the renormalization group method. The flow -equations and the free energy have been obtained for dimension d, and the cases d < 2 and d = 2 have been analysed in the limit of low and high temperatures. The critical temperature, the coherence length and the specific heat of a two dimensional Bose gas have been obtained using a solution for the coupling constant which does not present a singular behavior.

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We consider the transport and the noise characteristics for the case of a T-shape double-quantum-dot system using the equation of motion method. Our theoretical results, obtained in an approximation equivalent to the Hartree-Fock approximation, account for non-zero on-site Coulomb interaction in both the detector and side dots. The existence of a non-zero Coulomb interaction implies an additional two resonances in the detector's dot density of states and thereafter affects the electronic transport properties of the system. The system's conductance presents two Fano dips as a function of the energy of the localized electronic level in the side dot. The Fano dips in the system's conductance can be observed for both strong (fast detector) and weak coupling (slow detector) between the detector dot and the external electrodes. Due to stronger electronic correlations, the noise characteristics in the case of a slow detector are much higher. This setup may be of interest for the practical realization of qubit states in quantum dot systems.