Theory of plasmon-enhanced high-harmonic generation in the vicinity of metal nanostructures in noble gases

We present a semiclassical model for plasmon-enhanced high-harmonic generation (HHG) in the vicinity of metal nanostructures. We show that both the inhomogeneity of the enhanced local fields and electron absorption by the metal surface play an important role in the HHG process and lead to the generation of even harmonics and to a significantly increased cutoff. For the examples of silver-coated nanocones and bowtie antennas we predict that the required intensity reduces by up to three orders of magnitudes and the HHG cutoff increases by more than a factor of two. The study of the enhanced high-harmonic generation is connected with a finite-element simulation of the electric field enhancement due to the excitation of the plasmonic modes.Comment: 4 figure

Laboratory Bounds on Electron Lorentz Violation

Violations of Lorentz boost symmetry in the electron and photon sectors can be constrained by studying several different high-energy phenomenon. Although they may not lead to the strongest bounds numerically, measurements made in terrestrial laboratories produce the most reliable results. Laboratory bounds can be based on observations of synchrotron radiation, as well as the observed absences of vacuum Cerenkov radiation. Using measurements of synchrotron energy losses at LEP and the survival of TeV photons, we place new bounds on the three electron Lorentz violation coefficients c_(TJ), at the 3 x 10^(-13) to 6 x 10^(-15) levels.Comment: 18 page

Discrete concavity and the half-plane property

Murota et al. have recently developed a theory of discrete convex analysis which concerns M-convex functions on jump systems. We introduce here a family of M-concave functions arising naturally from polynomials (over a field of generalized Puiseux series) with prescribed non-vanishing properties. This family contains several of the most studied M-concave functions in the literature. In the language of tropical geometry we study the tropicalization of the space of polynomials with the half-plane property, and show that it is strictly contained in the space of M-concave functions. We also provide a short proof of Speyer's hive theorem which he used to give a new proof of Horn's conjecture on eigenvalues of sums of Hermitian matrices.Comment: 14 pages. The proof of Theorem 4 is corrected

Fracturing the optimal paths

Optimal paths play a fundamental role in numerous physical applications ranging from random polymers to brittle fracture, from the flow through porous media to information propagation. Here for the first time we explore the path that is activated once this optimal path fails and what happens when this new path also fails and so on, until the system is completely disconnected. In fact numerous applications can be found for this novel fracture problem. In the limit of strong disorder, our results show that all the cracks are located on a single self-similar connected line of fractal dimension $D_{b} \approx 1.22$. For weak disorder, the number of cracks spreads all over the entire network before global connectivity is lost. Strikingly, the disconnecting path (backbone) is, however, completely independent on the disorder.Comment: 4 pages,4 figure

Diffusion and spectral dimension on Eden tree

We calculate the eigenspectrum of random walks on the Eden tree in two and three dimensions. From this, we calculate the spectral dimension $d_s$ and the walk dimension $d_w$ and test the scaling relation $d_s = 2d_f/d_w$ ($=2d/d_w$ for an Eden tree). Finite-size induced crossovers are observed, whereby the system crosses over from a short-time regime where this relation is violated (particularly in two dimensions) to a long-time regime where the behavior appears to be complicated and dependent on dimension even qualitatively.Comment: 11 pages, Plain TeX with J-Phys.sty style, HLRZ 93/9