arXiv subjects
Publications and source records attributed to Michael Schreiber.
The h-index has been shown to have predictive power. Here I report results of an empirical study showing that the increase of the h-index with time often depends for a long time on citations to rather old publications. This inert behavior of the h-index means that it is difficult to use it as a measure for predicting future scientific output.
We study the properties of wave functions and the wave-packet dynamics in quasiperiodic tight-binding models in one, two, and three dimensions. The atoms in the one-dimensional quasiperiodic chains are coupled by weak and strong bonds aligned according to the Fibonacci sequence. The associated d-dimensional quasiperiodic tilings are constructed from the direct product of d such chains, which yields either the hypercubic tiling or the labyrinth tiling. This approach allows us to consider rather large systems numerically. We show that the wave functions of the system are multifractal and that their properties can be related to the structure of the system in the regime of strong quasiperiodic modulation by a renormalization group (RG) approach. We also study the dynamics of wave packets to get information about the electronic transport properties. In particular, we investigate the scaling behaviour of the return probability of the wave packet with time. Applying again the RG approach we show that in the regime of strong quasiperiodic modulation the return probability is governed by the underlying quasiperiodic structure. Further, we also discuss lower bounds for the scaling exponent of the width of the wave packet and propose a modified lower bound for the absolute continuous regime.
We study the electronic transport in quasiperiodic separable tight-binding models in one, two, and three dimensions. First, we investigate a one-dimensional quasiperiodic chain, in which the atoms are coupled by weak and strong bonds aligned according to the Fibonacci chain. The associated d-dimensional quasiperiodic tilings are constructed from the product of d such chains, which yields either the square/cubic Fibonacci tiling or the labyrinth tiling. We study the scaling behavior of the mean square displacement and the return probability of wave packets with respect to time. We also discuss results of renormalization group approaches and lower bounds for the scaling exponent of the width of the wave packet.
The eigenstates of d-dimensional quasicrystalline models with a separable Hamiltonian are studied within the tight-binding model. The approach is based on mathematical sequences, constructed by an inflation rule P = {w -> s, s -> sws^(b-1)} describing the weak/strong couplings of atoms in a quasiperiodic chain. Higher-dimensional quasiperiodic tilings are constructed as a direct product of these chains and their eigenstates can be directly calculated by multiplying the energies or wave functions of the chain, respectively. Applying this construction rule, the grid in d dimensions splits into 2^(d-1) different tilings, for which we investigated the characteristics of the wave functions. For the standard two-dimensional labyrinth tiling constructed from the octonacci sequence (b=2) the lattice breaks up into two identical lattices, which consequently yield the same eigenstates. While this is not the case for other b, our numerical results show that the wave functions of the different grids become increasingly similar for large system sizes. This can be explained by the fact that the structure of the 2^(d-1) grids mainly differs at the boundaries and thus for large systems the eigenstates approach each other. This property allows us to analytically derive properties of the higher-dimensional generalized labyrinth tilings from the one-dimensional results. In particular participation numbers and corresponding scaling exponents have been determined.
The light propagation through a stack of two media with different refractive indices, which are aligned according to different quasiperiodic sequences determined by metallic means, is studied using the transfer matrix method. The focus lies on the investigation of the influence of the underlying quasiperiodic sequence as well as the dependence of the transmission on the frequency, the incidence angle of the light wave and different ratios of the refractive indices. In contrast to a periodically aligned stack we find complete transmission for the quasiperiodic systems for a wide range of different refraction indices for small incidence angles. Additional bands of moderate transmission occur for frequencies in the range of the photonic band gaps of the periodic system. Further, for fixed indices of refraction we find a range of almost perfect transmission for angles close to the angle of total reflection, which is caused by the bending of photonic transmission bands towards higher frequencies for increasing incidence angles. Comparing with the results of a periodic stack the quasiperiodicity seems to have only an influence in the region around the midgap frequency of a periodic stack.
We compare different partitioning schemes for the box-counting algorithm in the multifractal analysis by computing the singularity spectrum and the distribution of the box probabilities. As model system we use the Anderson model of localization in two and three dimensions. We show that a partitioning scheme which includes unrestricted values of the box size and an average over all box origins leads to smaller error bounds than the standard method using only integer ratios of the linear system size and the box size which was found by Rodriguez et al. (Eur. Phys. J. B 67, 77-82 (2009)) to yield the most reliable results.
Absolute temperature, the fundamental temperature scale in thermodynamics, is usually bound to be positive. Under special conditions, however, negative temperatures - where high-energy states are more occupied than low-energy states - are also possible. So far, such states have been demonstrated in localized systems with finite, discrete spectra. Here, we were able to prepare a negative temperature state for motional degrees of freedom. By tailoring the Bose-Hubbard Hamiltonian we created an attractively interacting ensemble of ultracold bosons at negative temperature that is stable against collapse for arbitrary atom numbers. The quasi-momentum distribution develops sharp peaks at the upper band edge, revealing thermal equilibrium and bosonic coherence over several lattice sites. Negative temperatures imply negative pressures and open up new parameter regimes for cold atoms, enabling fundamentally new many-body states and counterintuitive effects such as Carnot engines above unity efficiency.
We study the quantum diffusion in quasiperiodic tight-binding models in one, two, and three dimensions. First, we investigate a class of one-dimensional quasiperiodic chains, in which the atoms are coupled by weak and strong bonds aligned according to the metallic-mean sequences. The associated generalized labyrinth tilings in d dimensions are then constructed from the direct product of d such chains, which allows us to consider rather large systems numerically. The electronic transport is studied by computing the scaling behavior of the mean-square displacement of the wave packets with respect to the time. The results reveal the occurrence of anomalous diffusion in these systems. By extending a renormalization group approach, originally proposed for the golden-mean chain, we show also for the silver-mean chain as well as for the higher-dimensional labyrinth tilings that in the regime of strong quasiperiodic modulation the wave-packet dynamics are governed by the underlying quasiperiodic structure.
In spontaneous emission an atom in an excited state undergoes a transition to the ground state and emits a single photon. Associated with the emission is a change of the atomic momentum due to photon recoil. Photon emission can be modified close to surfaces and in cavities. For an ion, localized in front of a mirror, coherence of the emitted resonance fluorescence has been reported. In free space experiments demonstrated that spontaneous emission destroys motional coherence. Here we report on motional coherence created by a single spontaneous emission event close to a mirror surface. The coherence in the free atomic motion is verified by atom interferometry. The photon can be regarded as a beamsplitter for an atomic matterwave and consequently our experiment extends the original recoiling slit Gedanken experiment by Einstein to the case where the slit is in a robust coherent superposition of the two recoils associated with the two paths of the quanta.
The recently proposed fractional scoring scheme is used to attribute publications to percentile rank classes. It is shown that in this way uncertainties and ambiguities in the evaluation of percentile ranks do not occur. Using the fractional scoring the total score of all papers exactly reproduces the theoretical value.
A percentile-based bibliometric indicator is an indicator that values publications based on their position within the citation distribution of their field. The most straightforward percentile-based indicator is the proportion of frequently cited publications, for instance the proportion of publications that belong to the top 10% most frequently cited of their field. Recently, more complex percentile-based indicators were proposed. A difficulty in the calculation of percentile-based indicators is caused by the discrete nature of citation distributions combined with the presence of many publications with the same number of citations. We introduce an approach to calculating percentile-based indicators that deals with this difficulty in a more satisfactory way than earlier approaches suggested in the literature. We show in a formal mathematical framework that our approach leads to indicators that do not suffer from biases in favor of or against particular fields of science.
From the quantum mechanical point of view, the electronic characteristics of quasicrystals are determined by the nature of their eigenstates. A practicable way to obtain information about the properties of these wave functions is studying the scaling behavior of the generalized inverse participation numbers $Z_q \sim N^{-D_q(q-1)}$ with the system size $N$. In particular, we investigate $d$-dimensional quasiperiodic models based on different metallic-mean quasiperiodic sequences. We obtain the eigenstates of the one-dimensional metallic-mean chains by numerical calculations for a tight-binding model. Higher dimensional solutions of the associated generalized labyrinth tiling are then constructed by a product approach from the one-dimensional solutions. Numerical results suggest that the relation $D_q^{d\mathrm{d}} = d D_q^\mathrm{1d}$ holds for these models. Using the product structure of the labyrinth tiling we prove that this relation is always satisfied for the silver-mean model and that the scaling exponents approach this relation for large system sizes also for the other metallic-mean systems.
It is shown that under certain circumstances in particular for small datasets the recently proposed citation impact indicators I3(6PR) and R(6,k) behave inconsistently when additional papers or citations are taken into consideration. Three simple examples are presented, in which the indicators fluctuate strongly and the ranking of scientists in the evaluated group is sometimes completely mixed up by minor changes in the data base. The erratic behavior is traced to the specific way in which weights are attributed to the six percentile rank classes, specifically for the tied papers. For 100 percentile rank classes the effects will be less serious. For the 6 classes it is demonstrated that a different way of assigning weights avoids these problems, although the non-linearity of the weights for the different percentile rank classes can still lead to (much less frequent) changes in the ranking. This behavior is not undesired, because it can be used to correct for differences in citation behavior in different fields. Remaining deviations from the theoretical value R(6,k) = 1.91 can be avoided by a new scoring rule, the fractional scoring. Previously proposed consistency criteria are amended by another property of strict independence which a performance indicator should aim at.
The spin-1 Heisenberg model on a triangular lattice with the ferromagnetic nearest, $J_1=-(1-p)J,$ $J>0$, and antiferromagnetic third-nearest-neighbor, $J_3=pJ$, exchange interactions is studied in the range of the parameter $0 \leqslant p \leqslant 1$. Mori's projection operator technique is used as a method, which retains the rotation symmetry of spin components and does not anticipate any magnetic ordering. For zero temperature several phase transitions are observed. At $p\approx 0.2$ the ground state is transformed from the ferromagnetic spin structure into a disordered state, which in its turn is changed to an antiferromagnetic long-range ordered state with the incommensurate ordering vector ${\bf Q = Q^\prime} \approx (1.16, 0)$ at $p\approx 0.31$. With the further growth of $p$ the ordering vector moves along the line ${\bf Q^\prime-Q_c}$ to the commensurate point ${\bf Q_c}=(\frac{2π}{3}, 0)$, which is reached at $p = 1$. The final state with an antiferromagnetic long-range order can be conceived as four interpenetrating sublattices with the $120^\circ$ spin structure on each of them. Obtained results are used for interpretation of the incommensurate magnetic ordering observed in NiGa$_2$S$_4$.
The possibility of driving an Anderson metal-insulator transition in the presence of scale-free disorder by changing the correlation exponent is numerically investigated. We calculate the localization length for quasi-one-dimensional systems at fixed energy and fixed disorder strength using a standard transfer matrix method. From a finite-size scaling analysis we extract the critical correlation exponent and the critical exponent characterizing the phase transition.
We study the influence of scale-free correlated disorder on the metal-insulator transition in the Anderson model of localization. We use standard transfer matrix calculations and perform finite-size scaling of the largest inverse Lyapunov exponent to obtain the localization length for respective 3D tight-binding systems. The density of states is obtained from the full spectrum of eigenenergies of the Anderson Hamiltonian. We discuss the phase diagram of the metal-insulator transition and the influence of the correlated disorder on the critical exponents.
The diamagnetism of confined Dirac fermions submitted to a uniform magnetic field in disordered graphene is investigated. The solutions of the energy spectrum are used to discuss the orbital magnetism from a statistical mechanical point of view. More precisely, by the technique of Green functions the self-energy for short and long-ranged disorders is obtained. This allows us to determine the susceptibility for short and long-ranged disorders together with confinement. We compare our results with already published work and point out the relevance of these findings to a systematic formulation of the diamagnetism in a confining potential.
Anderson localization has been a subject of intense studies for many years. In this context, we study numerically the influence of long-range correlated disorder on the localization behavior in one dimensional systems. We investigate the localization length and the density of states and compare our numerical results with analytical predictions. Specifically, we find two distinct characteristic behaviors in the vicinity of the band center and at the unperturbed band edge, respectively. Furthermore we address the effect of the intrinsic short-range correlations.