The Matsumoto and Yor process and infinite dimensional hyperbolic space

The Matsumoto\,--Yor process is $\int\_0^t \exp(2B\_s-B\_t)\, ds$, where $(B\_t)$ is a Brownian motion. It is shown that it is the limit of the radial part of the Brownian motion at the bottom of the spectrum on the hyperbolic space of dimension $q$, when $q$ tends to infinity. Analogous processes on infinite series of non compact symmetric spaces and on regular trees are described.Comment: 3

Littelmann paths and brownian paths

We study some path transformations related to Littelmann path model and their applications to representation theory and Brownian motion in a Weyl chamber.Comment: 30 pages, 1 figur

Pitman transforms and Brownian motion in the interval viewed as an affine alcove

Pitman's theorem states that if {Bt, t $\ge$ 0} is a one-dimensional Brownian motion, then {Bt -- 2 inf s$\le$t Bs, t $\ge$ 0} is a three dimensional Bessel process, i.e. a Brownian motion conditioned in Doob sense to remain forever positive. In this paper one gives a similar representation for the Brownian motion in an interval. Due to the double barrier, it is much more involved and only asymptotic. This uses the fact that the interval is an alcove of the Affine Lie algebra A 1 1

On the existence of some ARCH(∞\infty) processes

A new sufficient condition for the existence of a stationary causal solution of an ARCH($\infty$) equation is provided. This condition allows to consider polynomially decaying coefficients, so that it can be applied to the so-called FIGARCH processes, whose existence is thus proved

Photon correlation spectroscopy on a single quantum dot embedded in a nanowire

We have observed strong photoluminescence from a single CdSe quantum dot embedded in a ZnSe nanowire. Exciton, biexciton and charged exciton lines have been identified unambiguously using photon correlation spectroscopy. This technique has provided a detailed picture of the dynamics of this new system. This type of semi conducting quantum dot turns out to be a very efficient single photon source in the visible. Its particular growth technique opens new possibilities as compared to the usual self-asssembled quantum dots

Dark exciton optical spectroscopy of a semiconducting quantum dot embedded in a nanowire

Photoluminescence of a single CdSe quantum dot embedded in a ZnSe nanowire has been investigated. It has been found that the dark exciton has a strong influence on the optical properties. The most visible influence is the strongly reduced excitonic emission compared to the biexcitonic one. Temperature dependent lifetime measurements have allowed us to measure a large splitting of $\Delta E = 6$ meV between the dark and the bright exciton as well as the spin flip rates between these two states

Extraction of the homogeneous linewidth of the spectrally diffusing line of a CdSe/ZnSe quantum dot embedded in a nanowire

International audienceWe present a simple method to extract the homogeneous linewidth of a single photon emitter line exhibiting fast (down to 1 ns) spectral diffusion (SD). It is based on a recently developed technique using photon correlation measurements on half of the line. Here we show that the SD induced bunching depends on the ratio between the width of the homogeneous line and the spectral diffusion amplitude. Using this technique on a CdSe/ZnSe quantum dot, we investigate the temperature dependence of its fast SD amplitude and its homogeneous excitonic linewidt

Insertion of CdSe quantum dots in ZnSe nanowires: Correlation of structural and chemical characterization with photoluminescence

International audienceZnSe nanowires with CdSe quantum dot insertions were grown by molecular beam epitaxy using gold as a catalyst. Structural, chemical, and optical properties of the wires and quantum dots were characterized using electron microscopy and photoluminescence spectroscopy. We determined the crystalline structure, the chemical composition, and the size of the quantum dot and established a correlation between quantum dot size and luminescence. As expected, a blueshift of the luminescence was observed for decreasing quantum dot size. The comparison of calculated photoluminescence energy and experimental data seems to indicate that the quantum dots consist of a ZnxCd1-xSe ternary alloy rather than pure CdSe

Insertion of CdSe quantumdots in ZnSe nanowires : MBE growth and microstructure analysis

International audienceZnSe nanowire growth has been successfully achieved on ZnSe (100) and (111)B buffer layers deposited on GaAs substrates. Cubic [100] oriented ZnSe nanowires or [0001] oriented hexagonal NWs are obtained on (100) substrates while [111] oriented cubic mixed with [0001] oriented hexagonal regions are obtained on (111)B substrates. Most of the NWs are perpendicular to the surface in the last case. CdSe quantum dots were successfully incorporated in the ZnSe NWs as demonstrated by transmission electron microscopy, energy filtered TEM and high angle annular dark field scanning TEM measurements