Thermodynamics and Evaporation of the 2+1-D Black Hole

The properties of canonical and microcanonical ensembles of a black hole with thermal radiation and the problem of black hole evaporation in 3-D are studied. In 3-D Einstein-anti-de Sitter gravity we have two relevant mass scales, $m_c=1/G$, and $m_p=(\hbar^2\Lambda/G)^{1/3}$, which are particularly relevant for the evaporation problem. It is argued that in the `weak coupling' regime $\Lambda<(\hbar G)^{-2}$, the end point of an evaporating black hole formed with an initial mass $m_0>m_p$, is likely to be a stable remnant in equilibrium with thermal radiation. The relevance of these results for the information problem and for the issue of back reaction is discussed. In the `strong coupling' regime, $\Lambda>(\hbar G)^{-2}$ a full fledged quantum gravity treatment is required. Since the total energy of thermal states in anti-de Sitter space with reflective boundary conditions at spatial infinity is bounded and conserved, the canonical and microcanonical ensembles are well defined. For a given temperature or energy black hole states are locally stable. In the weak coupling regime black hole states are more probable then pure radiation states.Comment: 11 pages, TAUP 2141/94, Late

Nonlinear microrheology of dense colloidal suspensions: a mode-coupling theory

A mode-coupling theory for the motion of a strongly forced probe particle in a dense colloidal suspension is presented. Starting point is the Smoluchowski equation for $N$ bath and a single probe particle. The probe performs Brownian motion under the influence of a strong constant and uniform external force \Fex. It is immersed in a dense homogeneous bath of (different) particles also performing Brownian motion. Fluid and glass states are considered; solvent flow effects are neglected. Based on a formally exact generalized Green-Kubo relation, mode coupling approximations are performed and an integration through transients approach applied. A first-principles theory for the nonlinear velocity-force relations of the probe particle in a dense fluid and for the (de-) localized probe in a glass is obtained. It extends the mode coupling theory of the glass transition to strongly forced tracer motion and describes active microrheology experiments. A force threshold is identified which needs to be overcome to pull the probe particle free in a glass. For the model of hard sphere particles, the microscopic equations for the threshold force and the probability density of the localized probe are solved numerically. Neglecting the spatial structure of the theory, a schematic model is derived which contains two types of bifurcation, the glass transition and the force-induced delocalization, and which allows for analytical and numerical solutions. We discuss its phase diagram, forcing effects on the time-dependent correlation functions, and the friction increment. The model was successfully applied to simulations and experiments on colloidal hard sphere systems [I. Gazuz et. al., Phys. Rev. Lett. 102, 248302 (2009)], while we provide detailed information on its derivation and general properties.Comment: 24 pages, 14 figure

The transmetalation step in Pd-catalyzed processes: understanding the role of the classical nucleophile, the ligands and the synthetic potential of a third metal

The transmetalation step of Pd-catalyzed reactions is studied in-depth in this Doctoral Thesis. New bimetallic systems based on the Au/Pd and the Cu/Pd couple have been developed in the context of the Stille reaction and the Hiyama reaction that are very efficient for the coupling of bulky groups. This type of couplings are very challenging with other methodologies and provide excellent results under a synthetic point of view with our bimetallic approach. The bimetallic systems have been examined under a mechanistic point of view. The role of the cocatalyst, the auxiliary ligands and the tin and silicon organometallics have been understood, providing relevant information for the improvement of these systems and the development of new others. The secondary transmetalations that lead to undesired byproducts in the Negishi reaction have been studied in detail by experimental and computational techniques. The information obtained in our study provides important information that will contribute to develop more efficient Negishi reactions. A ligand designed in our group to promote challenging reductive eliminations has been tested for the Pd-catalyzed fluorination and trifluoromethylation of aryl halides. The ligand is not effective for this reaction due to the existence of a migratory insertion process that prevents the desired reductive elimination. This process has been studied by DFT calculations. The mechanisms of the N-H activation of anilines by Ir(PCP) complexes has been carried out by experimental and computational techniques. The information obtained will be used to design more efficient reactions based on this activation.Departamento de Química Física y Química InorgánicaDoctorado en Química: Química de Síntesis, Catálisis y Materiales Avanzado

Nanoscale mapping and control of antenna-coupling strength for bright single photon sources

Cavity QED is the art of enhancing light-matter interaction of photon emitters in cavities, with opportunities for sensing, quantum information and energy capture technologies. To boost emitter-cavity interaction, i.e. coupling strength , ultrahigh quality cavities have been concocted yielding photon trapping times of µs to ms. However, such high-Q cavities give poor photon output, hindering applications. To preserve high photon output it is advantageous to strive for highly localised electric fields in radiatively lossy cavities. Nanophotonic antennas are ideal candidates combining low-Q factors with deeply localised mode volumes, allowing large , provided the emitter is positioned exactly right inside the nanoscale mode volume. Here, with nanometre resolution, we map and tune the coupling strength between a dipole nanoantenna-cavity and a single molecule, obtaining a coupling rate of max ~ 200 GHz. Together with accelerated single photon output, this provides ideal conditions for fast and pure non-classical single photon emission with brightness exceeding 10E9 photons/sec. Clearly, nanoantennas acting as “bad” cavities offer an optimal regime for strong coupling , to deliver bright on-demand and ultrafast single photon nanosources for quantum technologies.Peer ReviewedPostprint (author's final draft