We develop a model for a simple order book and for the price evolution of an instrument traded on an exchange. The model can handle both stationary and highly non-stationary dynamics in the price of the instrument, including sudden and fast changes (“flash crash”). It also incorporates a feedback mechanism linked to the imbalance of the order book. Yet the model remains simple enough to allow for calculating results analytically. In particular, we derive an expression for the probability of the increase of the price. We also establish a versatile volume-based numerical simulation framework. The order processing rules can be changed flexibly to a great extent and different order generation and submission processes can also be simulated in a numerically fast way. We show via simulations that the feedback leads to sudden and large changes in the price. The crashes can equally go either down or up, which is a phenomenon observed in practice on real exchanges. Moreover, our simulation yields a crash in the price which is very similar to the real dynamics of Dow Jones Industrial Average during the flash crash. We also consider order books typical at exchanges using first-in-first-out order processing as well as characteristic books of exchanges where the orders are processed on a pro-rata basis. The price volatility is observed to be less sensitive to the feedback in the case of pro-rata order processing.

In a recent publication [Phys. Rev. Lett. 97, 227402 (2006)], it has been demonstrated numerically that a long-range disorder potential in a semiconductor quantum well can be reconstructed reliably via single-photon interferometry of spontaneously emitted light. In the present paper, a simplified analytical model of independent two-level systems is presented in order to study the reconstruction procedure in more detail. With the help of this model, the measured photon correlations can be calculated analytically and the influence of parameters, such as the disorder length scale, the wavelength of the used light, or the spotsize can be investigated systematically. Furthermore, the relation between the proposed angle-resolved single-photon correlations and the disorder potential can be understood and the measured signal is expected to be closely related to the characteristic strength and length scale of the disorder.

We study the relaxation of a non-equilibrium carrier distribution under the influence of the electron-electron interaction in the presence of disorder. Based on the Anderson model, our Hamiltonian is composed from a single particle part including the disorder and a two-particle part accounting for the Coulomb interaction. We apply the equation-of-motion approach for the density matrix, which provides a fully microscopic description of the relaxation. Our results show that the nonequlibrium distribution in this closed and internally interacting system relaxes exponentially fast during the initial dynamics. This fast relaxation can be described by a phenomenological damping rate. The total single particle energy decreases in the redistribution process, keeping the total energy of the system fixed. It turns out that the relaxation rate decreases with increasing disorder.

Angle and energy resolved single-photon correlation measurements of luminescence emitted from semiconductor nanostructures are modeled. A simple reconstruction procedure is shown to yield the long-range disorder fluctuations with high fidelity.

A microscopic theory for the luminescence of ordered semiconductors is modified to describe photoluminescence of strongly disordered semiconductors. The approach includes both diagonal disorder and the many-body Coulomb interaction. As a case study, the light emission of a correlated plasma is investigated numerically for a one-dimensional two-band tight-binding model. The band structure of the underlying ordered system is assumed to correspond to either a direct or an indirect semiconductor. In particular, luminescence and absorption spectra are computed for various levels of disorder and sample temperature to determine thermodynamic relations, the Stokes shift, and the radiative lifetime distribution.

The method of angular photonic correlations of spontaneous emission is introduced as an experimental, purely optical scheme to characterize disorder in semiconductor nanostructures. The theoretical expression for the angular correlations is derived and numerically evaluated for a model system. The results demonstrate how the proposed experimental method yields direct information about the spatial distribution of the relevant states and thus on the disorder present in the system.

Recently, a percolation analysis has been applied to describe potential decays on surfaces of corona-charged electrets [Yovcheva et al., J. Phys.: Condens. Matter 16, 455 (2004)]. In this analysis, a numerical method based on a "black-box" software was used, and this does not allow a transparent treatment of parameters responsible for the decays. We suggest an exact analytical solution of this theoretical problem, within the very same model as the one used by Yovcheva et al. The analytical solution provides a much better understanding of the potential decay phenomenon than a "black-box" numerical calculation.

From the recent analysis of the potential fluctuations in disordered semiconductors on the basis of optical and transport measurements [1] it was concluded that these two different kinds of phenomena evidence extremely different energy scales of the random potential in the same sample. We resolve this puzzle using for the analysis of experimental data the well-known theories of transport and optical absorption in a disordered system with long-range potential fluctuations, caused by charged impurities [2, 3]. The key point in our consideration is the essential difference between the density of states caused by the long-range fluctuations and the shape of the absorption coefficient. The latter is known to depend essentially not only on the fluctuation probability but also on the tunnelling efficiency of the optically excited electrons in the potential relief provided by the fluctuations [2]. (C) 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.