Existence of graphs with sub exponential transitions probability decay and applications

In this paper, we present a complete proof of the construction of graphs with bounded valency such that the simple random walk has a return probability at time $n$ at the origin of order $exp(-n^{\alpha}),$ for fixed $\alpha \in [0,1[$ and with Folner function $exp(n^{\frac{2\alpha}{1-\alpha}})$. We begin by giving a more detailled proof of this result contained in (see \cite{ershdur}). In the second part, we give an application of the existence of such graphs. We obtain bounds of the correct order for some functional of the local time of a simple random walk on an infinite cluster on the percolation model.Comment: 46 page

Intersections on tropical moduli spaces

This article explores to which extent the algebro-geometric theory of rational descendant Gromov-Witten invariants can be carried over to the tropical world. Despite the fact that the tropical moduli-spaces we work with are non-compact, the answer is surprisingly positive. We discuss the string, divisor and dilaton equations, we prove a splitting lemma describing the intersection with a "boundary" divisor and we prove general tropical versions of the WDVV resp. topological recursion equations (under some assumptions). As a direct application, we prove that the toric varieties $\mathbb{P}^1$, $\mathbb{P}^2$, $\mathbb{P}^1 \times \mathbb{P}^1$ and with Psi-conditions only in combination with point conditions, the tropical and classical descendant Gromov-Witten invariants coincide (which extends the result for $\mathbb{P}^2$ in Markwig-Rau-2008). Our approach uses tropical intersection theory and can unify and simplify some parts of the existing tropical enumerative geometry (for rational curves).Comment: 40 pages, 17 Postscript figures; updated to fit the published versio

A Microscopic Perspective on Photovoltaic Reciprocity in Ultrathin Solar Cells

The photovoltaic reciprocity theory relates the electroluminescence spectrum of a solar cell under applied bias to the external photovoltaic quantum efficiency of the device as measured at short circuit conditions. Its derivation is based on detailed balance relations between local absorption and emission rates in optically isotropic media with non-degenerate quasi-equilibrium carrier distributions. In many cases, the dependence of density and spatial variation of electronic and optical device states on the point of operation is modest and the reciprocity relation holds. In nanostructure-based photovoltaic devices exploiting confined modes, however, the underlying assumptions are no longer justifiable. In the case of ultrathin absorber solar cells, the modification of the electronic structure with applied bias is significant due to the large variation of the built-in field. Straightforward use of the external quantum efficiency as measured at short circuit conditions in the photovoltaic reciprocity theory thus fails to reproduce the electroluminescence spectrum at large forward bias voltage. This failure is demonstrated here by numerical simulation of both spectral quantities at normal incidence and emission for an ultrathin GaAs p-i-n solar cell using an advanced quantum kinetic formalism based on non-equilibrium Green's functions of coupled photons and charge carriers. While coinciding with the semiclassical relations under the conditions of their validity, the theory provides a consistent microscopic relationship between absorption, emission and charge carrier transport in photovoltaic devices at arbitrary operating conditions and for any shape of optical and electronic density of states.Comment: 5 pages, 4 figures, all figures replaced, minor changes and additions to the tex

Microscopic theory of absorption and emission in nanostructured solar cells: Beyond the generalized Planck formula

Absorption and emission in inorganic bipolar solar cells based on low dimensional structures exhibiting the effects of quantum confinement is investigated in the framework of a comprehensive microscopic theory of the optical and electronic degrees of freedom of the photovoltaic system. In a quantum-statistical treatment based on non-equilibrium Green's functions, the optical transition rates are related to the conservation of electronic currents, providing a quantum version of the balance equations describing the operation of a photovoltaic device. The generalized Planck law used for the determination of emission from an excited semiconductor in quasi-equilibrium is replaced by an expression of extended validity, where no assumptions on the distribution of electrons and photons are made. The theory is illustrated by the numerical simulation of single quantum well diodes at the radiative limit.Comment: 6 pages, 5 figures, extended LaTeX version of the EUPVSEC09 proceedings articl

Comptonization, the X-ray-radio correlation and the long-term periodicity in the chi-states of GRS 1915+105

We analyzed 139 chi-state observations of GRS 1915+105 with RXTE from 1997 to 2000 and found i) that the observations fall into two groups with different Comptonization behavior, ii) that the slope of the hard X-ray component correlates with the radio flux, thus revealing the interaction of jet and corona, and iii) a 590 days long term periodicity in the hard X-ray and radio components.Comment: 4 pages, 3 figures, Proceedings of the 4th Microquasar Workshop, 2002, eds. Durouchoux, Fuchs, & Rodriguez, published by the Center for Space Physics: Kolkat