Reflected Brownian motions in the KPZ universality class

This book presents a detailed study of a system of interacting Brownian motions in one dimension. The interaction is point-like such that the $n$-th Brownian motion is reflected from the Brownian motion with label $n-1$. This model belongs to the Kardar-Parisi-Zhang (KPZ) universality class. In fact, because of the singular interaction, many universal properties can be established with rigor. They depend on the choice of initial conditions. Discussion addresses packed and periodic initial conditions, stationary initial conditions, and mixtures thereof. The suitably scaled spatial process will be proven to converge to an Airy process in the long time limit. A chapter on determinantal random fields and another one on Airy processes are added to have the notes self-contained. This book serves as an introduction to the KPZ universality class, illustrating the main concepts by means of a single model only. It will be of interest to readers from interacting diffusion processes and non-equilibrium statistical mechanics.Comment: arXiv admin note: text overlap with arXiv:1502.0146

Anomalous molecular orbital variation upon adsorption on wide band gap insulator

It is commonly believed that organic molecules are physisorbed on the ideal non-polar surfaces of wide band gap insulators with limited variation of the electronic properties of the adsorbate molecule. On the basis of first principles calculations within density functional theory (DFT) and $GW$ approximation, we show that this is not generally true. We find that the molecular frontier orbitals undergo significant changes when a hydroxy acid (here we chose gluconic acid) is adsorbed on MgSO$_4$$\cdot$H$_2$O(100) surface due to the complex interaction between the molecule and the insulating surface. The predicted trend of the adsorption effect on the energy gap obtained by DFT is reversed when the surface polarization effect is taken into account via the many-body corrections.Comment: 5 pages, 3 figure

Magnon transport and spin current switching through quantum dots

We study the nonequilibrium spin current through a quantum dot consisting of two localized spin-1/2 coupled to two ferromagnetic insulators. The influence of an intra-dot magnetic field and exchange coupling, different dot-reservoir coupling configurations, and the influence of magnon chemical potential differences vs. magnetic field gradients onto the spin current are examined. We discuss various spin switching mechanisms and find that, in contrast to electronic transport, the spin current is very sensitive to the specific coupling configuration and band edges. In particular, we identify 1- and 2-magnon transport processes which can lead to resonances and antiresonances for the spin current.Comment: 10 pages, 15 figure

A Space-Time Discontinuous Galerkin Trefftz Method for time dependent Maxwell's equations

We consider the discretization of electromagnetic wave propagation problems by a discontinuous Galerkin Method based on Trefftz polynomials. This method fits into an abstract framework for space-time discontinuous Galerkin methods for which we can prove consistency, stability, and energy dissipation without the need to completely specify the approximation spaces in detail. Any method of such a general form results in an implicit time-stepping scheme with some basic stability properties. For the local approximation on each space-time element, we then consider Trefftz polynomials, i.e., the subspace of polynomials that satisfy Maxwell's equations exactly on the respective element. We present an explicit construction of a basis for the local Trefftz spaces in two and three dimensions and summarize some of their basic properties. Using local properties of the Trefftz polynomials, we can establish the well-posedness of the resulting discontinuous Galerkin Trefftz method. Consistency, stability, and energy dissipation then follow immediately from the results about the abstract framework. The method proposed in this paper therefore shares many of the advantages of more standard discontinuous Galerkin methods, while at the same time, it yields a substantial reduction in the number of degrees of freedom and the cost for assembling. These benefits and the spectral convergence of the scheme are demonstrated in numerical tests

Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems

We investigate a generalised version of the recently proposed ordinal partition time series to network transformation algorithm. Firstly we introduce a fixed time lag for the elements of each partition that is selected using techniques from traditional time delay embedding. The resulting partitions define regions in the embedding phase space that are mapped to nodes in the network space. Edges are allocated between nodes based on temporal succession thus creating a Markov chain representation of the time series. We then apply this new transformation algorithm to time series generated by the R\"ossler system and find that periodic dynamics translate to ring structures whereas chaotic time series translate to band or tube-like structures -- thereby indicating that our algorithm generates networks whose structure is sensitive to system dynamics. Furthermore we demonstrate that simple network measures including the mean out degree and variance of out degrees can track changes in the dynamical behaviour in a manner comparable to the largest Lyapunov exponent. We also apply the same analysis to experimental time series generated by a diode resonator circuit and show that the network size, mean shortest path length and network diameter are highly sensitive to the interior crisis captured in this particular data set