AdS and Lifshitz black hole solutions in conformal gravity sourced with a scalar field

In this paper we obtain exact asymptotically anti-de Sitter black hole solutions and asymptotically Lifshitz black hole solutions with dynamical exponents $z=0$ and $z=4$ of four-dimensional conformal gravity coupled with a self-interacting conformally invariant scalar field. Then, we compute their thermodynamical quantities, such as the mass, the Wald entropy and the Hawking temperature. The mass expression is obtained by using the generalized off-shell Noether potential formulation. It is found that the anti-de Sitter black holes as well as the Lifshitz black holes with $z=0$ have zero mass and zero entropy, although they have non-zero temperature. A similar behavior has been observed in previous works, where the integration constant is not associated with a conserved charge, and it can be interpreted as a kind of gravitational hair. On the other hand, the Lifshitz black holes with dynamical exponent $z=4$ have non-zero conserved charges, and the first law of black hole thermodynamics holds. Also, we analyze the horizon thermodynamics for the Lifshitz black holes with $z=4$, and we show that the first law of black hole thermodynamics arises from the field equations evaluated on the horizon. Furthermore, we study the propagation of a conformally coupled scalar field on these backgrounds and we find the quasinormal modes analytically in several cases. We find that for anti-de Sitter black holes and Lifshitz black holes with $z=4$, there is a continuous spectrum of frequencies for Dirichlet boundary condition; however, we show that discrete sets of well defined quasinormal frequencies can be obtained by considering Neumann boundary conditions

Driven-Dissipative Conductance in Nanojunction Arrays: Negative Conductance and Light-Induced Currents

Stationary coherence in small conducting arrays has been shown to influence the transport efficiency of electronic nanodevices. Model schemes that capture the interplay between electron delocalization and system-reservoir interactions on the device performance are therefore important for designing next-generation nanojunctions powered by quantum coherence. We use a Lindblad open quantum system approach to obtain the current-voltage characteristics of small-size networks of interacting conducting sites subject to radiative and non-radiative interactions with the environment, for experimentally-relevant case studies. Lindblad theory is shown to reproduce recent measurements of negative conductance in single-molecule junctions using a biased two-site model driven by thermal fluctuations. For array sites with conducting ground and excited orbitals in the presence of radiative incoherent pumping, we show that Coulomb interactions that otherwise suppress charge transport can be overcome to produce light-induced currents. We also show that in nanojunctions having asymmetric transfer rates between the array and electrical contacts, an incoherent driving field can induce photocurrents at zero bias voltage whose direction depend on the type or orbital delocalization established between sites. Possible extensions of the theory are discussed.Comment: 7 pages, 6 figure