On Eigenvalue spacings for the 1-D Anderson model with singular site distribution

We study eigenvalue spacings and local eigenvalue statistics for 1D lattice Schrodinger operators with Holder regular potential, obtaining a version of Minami's inequality and Poisson statistics for the local eigenvalue spacings. The main additional new input are regular properties of the Furstenberg measures and the density of states obtained in some of the author's earlier work.Comment: 13 page

Subnanosecond spectral diffusion of a single quantum dot in a nanowire

We have studied spectral diffusion of the photoluminescence of a single CdSe quantum dot inserted in a ZnSe nanowire. We have measured the characteristic diffusion time as a function of pumping power and temperature using a recently developed technique [G. Sallen et al, Nature Photon. \textbf{4}, 696 (2010)] that offers subnanosecond resolution. These data are consistent with a model where only a \emph{single} carrier wanders around in traps located in the vicinity of the quantum dot

Subnanosecond spectral diffusion measurement using photon correlation

Spectral diffusion is a result of random spectral jumps of a narrow line as a result of a fluctuating environment. It is an important issue in spectroscopy, because the observed spectral broadening prevents access to the intrinsic line properties. However, its characteristic parameters provide local information on the environment of a light emitter embedded in a solid matrix, or moving within a fluid, leading to numerous applications in physics and biology. We present a new experimental technique for measuring spectral diffusion based on photon correlations within a spectral line. Autocorrelation on half of the line and cross-correlation between the two halves give a quantitative value of the spectral diffusion time, with a resolution only limited by the correlation set-up. We have measured spectral diffusion of the photoluminescence of a single light emitter with a time resolution of 90 ps, exceeding by four orders of magnitude the best resolution reported to date

Retrieving information from subordination

We show that if $(X_s, s\geq 0)$ is a right-continuous process, Y_t=\int_0^t\d s X_s its integral process and $\tau = (\tau_{\ell}, \ell \geq 0)$ a subordinator, then the time-changed process $(Y_{\tau_{\ell}}, \ell\geq 0)$ allows to retrieve the information about $(X_{\tau_{\ell}}, \ell\geq 0)$ when $\tau$ is stable, but not when $\tau$ is a gamma subordinator. This question has been motivated by a striking identity in law involving the Bessel clock taken at an independent inverse Gaussian variable