Electron Transfer Reaction Through an Adsorbed Layer

We consider electron transfer from a redox to an electrode through and adsorbed intermediate. The formalism is developed to cover all regimes of coverage factor, from lone adsorbate to monolayer regime. The randomness in the distribution of adsorbates is handled using coherent potential approximation. We give current-overpotential profile for all coverage regimes. We explictly analyse the low and high coverage regimes by supplementing with DOS profile for adsorbate in both weakly coupled and strongly coupled sector. The prominence of bonding and anti-bonding states in the strongly coupled adsorbates at low coverage gives rise to saddle point behaviour in current-overpotential profile. We were able to recover the marcus inverted region at low coverage and the traditional direct electron transfer behaviour at high coverage

Graviton resonances on two-field thick branes

This work presents new results about the graviton massive spectrum in two-field thick branes. Analyzing the massive spectra with a relative probability method we have firstly showed the presence of resonance structures and obtained a connection between the thickness of the defect and the lifetimes of such resonances. We obtain another interesting results considering the degenerate Bloch brane solutions. In these thick brane models, we have the emergence of a splitting effect controlled by a degeneracy parameter. When the degeneracy constant tends to a critical value, we have found massive resonances to the gravitational field indicating the existence of modes highly coupled to the brane. We also discussed the influence of the brane splitting effect over the resonance lifetimes.Comment: 15 pages, 8 figure

Gravity localization on hybrid branes

This work deals with gravity localization on codimension-1 brane worlds engendered by compacton-like kinks, the so-called hybrid branes. In such scenarios, the thin brane behaviour is manifested when the extra dimension is outside the compact domain, where the energy density is non-trivial, instead of asymptotically as in the usual thick brane models. The zero mode is trapped in the brane, as required. The massive modes, although are not localized in the brane, have important phenomenological implications such as corrections to the Newton's law. We study such corrections in the usual thick domain wall and in the hybrid brane scenarios. By means of suitable numerical methods, we attain the mass spectrum for the graviton and the corresponding wavefunctions. The spectra possess the usual linearly increasing behaviour from the Kaluza-Klein theories. Further, we show that the 4D gravitational force is slightly increased at short distances. The first eigenstate contributes highly for the correction to the Newton's law. The subsequent normalized solutions have diminishing contributions. Moreover, we find out that the phenomenology of the hybrid brane is not different from the usual thick domain wall. The use of numerical techniques for solving the equations of the massive modes is useful for matching possible phenomenological measurements in the gravitational law as a probe to warped extra dimensions.Comment: 15 pages, 11 figure

Antisymmetric tensor propagator with spontaneous Lorentz violation

In this work, we study the spontaneous Lorentz symmetry breaking due to an antisymmetric 2-tensor field in Minkowski spacetime. For a smooth quadratic potential, the spectrum of the theory exhibits massless and massive excitations. We show that the equations of motion for the free field obey some constraints which lead to the massive mode be non-propagating at leading order. Besides, there exists a massless mode in the theory which can be identified with the usual Kalb-Ramond field, carrying only one on-shell degree of freedom. The same conclusion holds when one analyses the pole structure of its Feynman propagator. A new complete set of spin-type operators is found, which was the requirement to evaluate the propagator of the Kalb-Ramond field modified by the presence of a nonzero vacuum expectation value responsible for the Lorentz violation.Comment: 13 pages. Some modifications to match published version in EuroPhysics Letter

Finite element approximation of the p(⋅)p(\cdot)-Laplacian

We study a~priori estimates for the Dirichlet problem of the $p(\cdot)$-Laplacian, $$-\mathrm{div}(|\nabla v|^{p(\cdot)-2} \nabla v) = f.$$ We show that the gradients of the finite element approximation with zero boundary data converges with rate $O(h^\alpha)$ if the exponent $p$ is $\alpha$-H\"{o}lder continuous. The error of the gradients is measured in the so-called quasi-norm, i.e. we measure the $L^2$-error of $|\nabla v|^{\frac{p-2}{2}} \nabla v$

Orbital magnetism in axially deformed sodium clusters: From scissors mode to dia-para magnetic anisotropy

Low-energy orbital magnetic dipole excitations, known as scissors mode (SM), are studied in alkali metal clusters. Subsequent dynamic and static effects are explored. The treatment is based on a self-consistent microscopic approach using the jellium approximation for the ionic background and the Kohn-Sham mean field for the electrons. The microscopic origin of SM and its main features (structure of the mode in light and medium clusters, separation into low- and high-energy plasmons, coupling high-energy M1 scissors and E2 quadrupole plasmons, contributions of shape isomers, etc) are discussed. The scissors M1 strength acquires large values with increasing cluster size. The mode is responsible for the van Vleck paramagnetism of spin-saturated clusters. Quantum shell effects induce a fragile interplay between Langevin diamagnetism and van Vleck paramagnetism and lead to a remarkable dia-para anisotropy in magnetic susceptibility of particular light clusters. Finally, several routes for observing the SM experimentally are discussed.Comment: 21 pages, 7 figure