The growth exponent for planar loop-erased random walk

We give a new proof of a result of Kenyon that the growth exponent for loop-erased random walks in two dimensions is 5/4. The proof uses the convergence of LERW to Schramm-Loewner evolution with parameter 2, and is valid for irreducible bounded symmetric random walks on any two-dimensional discrete lattice.Comment: 62 pages, 7 figures; fixed typos, added reference

A supersonic crowdion in mica: Ultradiscrete kinks with energy between 40^{40}K recoil and transmission sputtering

In this chapter we analyze in detail the behaviour and properties of the kinks found in an one dimensional model for the close packed rows of potassium ions in mica muscovite. The model includes realistic potentials obtained from the physics of the problem, ion bombardment experiments and molecular dynamics fitted to experiments. These kinks are supersonic and have an unique velocity and energy. They are ultradiscrete involving the translation of an interstitial ion, which is the reason they are called 'crowdions'. Their energy is below the most probable source of energy, the decay of the $^{40}$K isotope and above the energy needed to eject an atom from the mineral, a phenomenon that has been observed experimentallyComment: 28 pages, 15 figure

Photochromism in single nitrogen-vacancy defect in diamond

Photochromism in single nitrogen-vacancy optical centers in diamond is demonstrated. Time-resolved optical spectroscopy shows that intense irradiation at 514 nm switches the nitrogen-vacancy defects to the negative form. This defect state relaxes back to the neutral form under dark conditions. Temporal anticorrelation of photons emitted by the different charge states of the optical center unambiguously indicates that the nitrogen-vacancy defect accounts for both 575 nm and 638 nm emission bands. Possible mechanism of photochromism involving nitrogen donors is discussed.Comment: 11 pages, 3 figures, submitted to Applied Physics B: Lasers and Optic