Interference of quantum critical excitations and soft diffusive modes in a disordered antiferromagnetic metal

We study the temperature-dependent quantum correction to conductivity due to the interplay of spin density fluctuations and weak disorder for a two-dimensional metal near an antiferromagnetic (AFM) quantum critical point. AFM spin density fluctuations carry large momenta around the ordering vector $\mathbf{Q}$ and, at lowest order of the spin-fermion coupling, only scatter electrons between "hot spots" of the Fermi surface which are connected by $\mathbf{Q}$. Earlier, it was seen that the quantum interference between AFM spin density fluctuations and soft diffusive modes of the disordered metal is suppressed, a consequence of the large-momentum scattering. The suppression of this interference results in a non-singular temperature dependence of the corresponding interaction correction to conductivity. However, at higher order of the spin-fermion coupling, electrons on the entire Fermi surface can be scattered successively by two spin density fluctuations and, in total, suffer a small momentum transfer. This higher-order process can be described by composite modes which carry small momenta. We show that the interference between formally subleading composite modes and diffusive modes generates singular interaction corrections which ultimately dominate over the non-singular first-order correction at low temperatures. We derive an effective low-energy theory from the spin-fermion model which includes the above-mentioned higher-order process implicitly and show that for weak spin-fermion coupling the small-momentum transfer is mediated by a composite propagator. Employing the conventional diagrammatic approach to impurity scattering, we find the correction $\delta \sigma \sim +\ln^2 T$ for temperatures above an exponentially small crossover scale.Comment: 13 pages, 7 figures. Published versio

Anwendungsorientierte Einführung in die Integralrechnung

Ausarbeitung eines Workshops der T³-Regionaltagung vom 08.11.2003 am Einhard-Gymnasium in Aachen.  Aus der Einleitung: "Die Einführung in die Integralrechnung wird meistens anhand eines Problems aus der Flächenberechnung durchgeführt, und auch in den Übungsaufgaben treten überwiegend Flächenberechnungen auf. Hier soll ein Zugang zur Integralrechnung vorgestellt werden, der von Beginn an auch andere Anwendungen wie Volumina, Mantelflächen und Bogenlängen einbezieht. Der Begriff Integral wird dabei so früh benutzt, dass im Unterricht mehrfach der Übergang von der Summation zur Integration erfolgen kann."</div

Quantum Fluctuations and Hydrodynamic Noise in Low Dimensions

Our theoretical work is organized in two independent parts: Part I belongs to the field of condensed matter theory and deals with the spectral signatures of collective states in one dimensional (1D) metals: Electrons in 1D metals are expected to fractionalize into collective spin and charge degrees of freedom. A recent candidate material for the realization of a 1D metal are mirror-twin boundaries in monolayer MoS2. Scanning tunneling spectroscopy was used to record the local density of states along these 1D line defects. In our purely theoretical work, we calculate the local density of states as predicted by Tomonaga-Luttinger-liquid theory in order to reveal the nature of the 1D states spectroscopically. The comparison of measured and theoretical spectra allows us to identify the observed doubling of the energy levels as signature of emergent spin and charge excitations. Part II belongs to the field of non-equilibrium physics and deals with the macroscopic description of equilibration: Equilibration of closed systems is hampered by the diffusive transport of locally conserved quantities as described by fluctuating hydrodynamics. After a sudden perturbation, the buildup of equilibrium fluctuations occurs only algebraically slowly, giving rise to hydrodynamic long-time tails. However, the standard tool in transport theory, the Boltzmann equation, fails to describe equilibration. Adding a noise term restores the missing correlations, resulting in a stochastic Langevin-Boltzmann equation. In our work, we derive a simplified version: a fluctuating relaxation-time approximation. We also set up a stable integration scheme for this type of equation and demonstrate that the numerical solution is in agreement with the predictions of fluctuating hydrodynamics. As an addition, we discuss slow changes of state. We show that the entropy production vanishes algebraically slowly in the adiabatic limit due to the presence of hydrodynamic slow modes

Correlating the nanostructure of Al-oxide with deposition conditions and dielectric contributions of two-level systems in perspective of superconducting quantum circuits

This work is concerned with Al/Al-oxide(AlO$_{x}$)/Al-layer systems which are important for Josephson-junction-based superconducting devices such as quantum bits. The device performance is limited by noise, which has been to a large degree assigned to the presence and properties of two-level tunneling systems in the amorphous AlO$_{x}$ tunnel barrier. The study is focused on the correlation of the fabrication conditions, nanostructural and nanochemical properties and the occurrence of two-level tunneling systems with particular emphasis on the AlO$_{x}$-layer. Electron-beam evaporation with two different processes and sputter deposition were used for structure fabrication, and the effect of illumination by ultraviolet light during Al-oxide formation is elucidated. Characterization was performed by analytical transmission electron microscopy and low-temperature dielectric measurements. We show that the fabrication conditions have a strong impact on the nanostructural and nanochemical properties of the layer systems and the properties of two-level tunneling systems. Based on the understanding of the observed structural characteristics, routes are derived towards the fabrication of Al/AlO$_{x}$/Al-layers systems with improved properties.Comment: 28 pages, 4 figure

Open Shop Scheduling with Synchronization

In this paper, we study open shop scheduling problems with synchronization. This model has the same features as the classical open shop model, where each of the n jobs has to be processed by each of the m machines in an arbitrary order. Unlike the classical model, jobs are processed in synchronous cycles, which means that the m operations of the same cycle start at the same time. Within one cycle, machines which process operations with smaller processing times have to wait until the longest operation of the cycle is finished before the next cycle can start. Thus, the length of a cycle is equal to the maximum processing time of its operations. In this paper, we continue the line of research started by Weiß et al. (Discrete Appl Math 211:183–203, 2016). We establish new structural results for the two-machine problem with the makespan objective and use them to formulate an easier solution algorithm. Other versions of the problem, with the total completion time objective and those which involve due dates or deadlines, turn out to be NP-hard in the strong sense, even for m=2 machines. We also show that relaxed models, in which cycles are allowed to contain less than m jobs, have the same complexity status

Steering random walks with kicked ultracold atoms

A kicking sequence of the atom optics kicked rotor at quantum resonance can be interpreted as a quantum random walk in momentum space. We show how to steer such a random walk by applying a random sequence of intensities and phases of the kicking lattice chosen according to a probability distribution. This distribution converts on average into the final momentum distribution of the kicked atoms. In particular, it is shown that a power-law distribution for the kicking strengths results in a L\'evy walk in momentum space and in a power-law with the same exponent in the averaged momentum distribution. Furthermore, we investigate the stability of our predictions in the context of a realistic experiment with Bose-Einstein condensates.Comment: detailed study of random walks and their implementation with a Bose condensate, 12 pages, 7 figure

The ARGUS Vertex Trigger

A fast second level trigger has been developed for the ARGUS experiment which recognizes tracks originating from the interaction region. The processor compares the hits in the ARGUS Micro Vertex Drift Chamber to 245760 masks stored in random access memories. The masks which are fully defined in three dimensions are able to reject tracks originating in the wall of the narrow beampipe of 10.5\,mm radius.Comment: gzipped Postscript, 27 page

The neutron time-of-flight facility n-TOF at CERN: Phase II

Neutron-induced reactions are studied at the neutron time-of-flight facility n-TOF at CERN. The facility uses 6∼ns wide pulses of 20 GeV/c protons impinging on a lead spallation target. The large neutron energy range and the high instantaneous neutron flux combined with high resolution are among the key characteristics of the facility. After a first phase of data taking during the period 2001-2004, the facility has been refurbished with an upgraded spallation target and cooling system for a second phase of data taking which started in 2009. Since 2010, the experimental area at 185 m where the neutron beam arrives, has been modified into a worksector of type A, allowing the extension of the physics program to include neutron-induced reactions on radioactive isotopes

Effects of Diversity on Multi-agent Systems: Minority Games

We consider a version of large population games whose agents compete for resources using strategies with adaptable preferences. The games can be used to model economic markets, ecosystems or distributed control. Diversity of initial preferences of strategies is introduced by randomly assigning biases to the strategies of different agents. We find that diversity among the agents reduces their maladaptive behavior. We find interesting scaling relations with diversity for the variance and other parameters such as the convergence time, the fraction of fickle agents, and the variance of wealth, illustrating their dynamical origin. When diversity increases, the scaling dynamics is modified by kinetic sampling and waiting effects. Analyses yield excellent agreement with simulations.Comment: 41 pages, 16 figures; minor improvements in content, added references; to be published in Physical Review