The dynamical equation of the spinning electron

We obtain by invariance arguments the relativistic and non-relativistic invariant dynamical equations of a classical model of a spinning electron. We apply the formalism to a particular classical model which satisfies Dirac's equation when quantised. It is shown that the dynamics can be described in terms of the evolution of the point charge which satisfies a fourth order differential equation or, alternatively, as a system of second order differential equations by describing the evolution of both the center of mass and center of charge of the particle. As an application of the found dynamical equations, the Coulomb interaction between two spinning electrons is considered. We find from the classical viewpoint that these spinning electrons can form bound states under suitable initial conditions. Since the classical Coulomb interaction of two spinless point electrons does not allow for the existence of bound states, it is the spin structure that gives rise to new physical phenomena not described in the spinless case. Perhaps the paper may be interesting from the mathematical point of view but not from the point of view of physics.Comment: Latex2e, 14 pages, 5 figure

Observation of a tricritical wedge filling transition in the 3D Ising model

In this Letter we present evidences of the occurrence of a tricritical filling transition for an Ising model in a linear wedge. We perform Monte Carlo simulations in a double wedge where antisymmetric fields act at the top and bottom wedges, decorated with specific field acting only along the wegde axes. A finite-size scaling analysis of these simulations shows a novel critical phenomenon, which is distinct from the critical filling. We adapt to tricritical filling the phenomenological theory which successfully was applied to the finite-size analysis of the critical filling in this geometry, observing good agreement between the simulations and the theoretical predictions for tricritical filling.Comment: 5 pages, 3 figure

Power-law decay in first-order relaxation processes

Starting from a simple definition of stationary regime in first-order relaxation processes, we obtain that experimental results are to be fitted to a power-law when approaching the stationary limit. On the basis of this result we propose a graphical representation that allows the discrimination between power-law and stretched exponential time decays. Examples of fittings of magnetic, dielectric and simulated relaxation data support the results.Comment: to appear in Phys. Rev. B; 4 figure

Collective resonances in plasmonic crystals: Size matters

Periodic arrays of metallic nanoparticles may sustain Surface Lattice Resonances (SLRs), which are collective resonances associated with the diffractive coupling of Localized Surface Plasmon Resonances (LSPRs). By investigating a series of arrays with varying number of particles, we traced the evolution of SLRs to its origins. Polarization resolved extinction spectra of arrays formed by a few nanoparticles were measured, and found to be in very good agreement with calculations based on a coupled dipole model. Finite size effects on the optical properties of the arrays are observed, and our results provide insight into the characteristic length scales for collective plasmonic effects: for arrays smaller than 5 x 5 particles, the Q-factors of SLRs are lower than those of LSPRs; for arrays larger than 20 x 20 particles, the Q-factors of SLRs saturate at a much larger value than those of LSPRs; in between, the Q-factors of SLRs are an increasing function of the number of particles in the array.Comment: 4 figure

Lanthanide(III) complexes of rhodamine-DO3A conjugates as agents for dual-modal imaging

Two novel dual-modal MRI/optical probes based on a rhodamine-DO3A conjugate have been prepared. The bis aqua-Gd(III) complex Gd.L1 and mono aqua-Gd(III) complex Gd.L2 behave as dual-modal imaging probes (r1 = 8.5 and 3.8 mM-1s-1 for Gd.L1 and Gd.L2 respectively; λex = 560 nm and λem = 580 nm for both complexes). The rhodamine fragment is pH sensitive and upon lowering of pH an increase in fluorescence intensity is observed as the spirolactam ring opens to give the highly fluorescent form of the molecule. The ligands are bimodal when coordinated to Tb(III) ions, inducing fluorescence from both the lanthanide center and the rhodamine fluorophore, on two independent time-frames. Confocal imaging experiments were carried out to establish the localization of Gd.L2 in HEK cells. Co-localisation with MitoTracker® Green confirmed that Gd.L2 compartmentalizes in the mitochondria. Gd.L2 was also evaluated as an MRI probe for imaging tumors in BALB/c nude mice bearing M21 xenografts. A 36.5% decrease in T1 within the tumor was observed 30 minutes post injection showing that Gd.L2 is preferentially up taken in the tumor. Gd.L2 is the first small molecule MR/fluorescent dual-modal imaging agent to display an off-on pH switch upon its preferential uptake within the more acidic micro-environment of tumor cells