We review recent evidence indicating that researchers in experimental psychology may have used suboptimal estimates of word frequency. Word frequency measures should be based on a corpus of at least 20 million words that contains language participants in psychology experiments are likely to have been exposed to. In addition, the quality of word frequency measures should be ascertained by correlating them with behavioral word processing data. When we apply these criteria to the word frequency measures available for the German language, we find that the commonly used Celex frequencies are the least powerful to predict lexical decision times. Better results are obtained with the Leipzig frequencies, the dlexDB frequencies, and the Google Books 2000-2009 frequencies. However, as in other languages the best performance is observed with subtitle-based word frequencies. The SUBTLEX-DE word frequencies collected for the present ms are made available in easy-to-use files and are free for educational purposes.

We derive a semiclassical time evolution kernel and a trace formula for the Dirac equation. The classical trajectories that enter the expressions are determined by the dynamics of relativistic point particles. We carefully investigate the transport of the spin degrees of freedom along the trajectories which can be understood geometrically as parallel transport in a vector bundle with SU(2) holonomy. Furthermore, we give an interpretation in terms of a classical spin vector that is transported along the trajectories and whose dynamics, dictated by the equation of Thomas precession, gives rise to dynamical and geometric phases every orbit is weighted by. We also present an analogous approach to the Pauli equation which we analyse in two different limits.

Recently, researchers reported a bias for placing agents predominantly on the left side of pictures. Both hemispheric specialization and cultural preferences have been hypothesized to be the origin of this bias. To evaluate these hypotheses, we conducted a study with participants exposed to different reading and writing systems: Germans, who use a left-to-right system, and Israelis, who use a right-to-left system. In addition, we manipulated the degree of exposure to the writing systems by testing preschoolers and adults. Participants heard agent-first or recipient-first sentences and were asked to draw the content of the sentences or to arrange transparencies of protagonists and objects such that their arrangement depicted the sentences. Although preschool-age children in both countries showed no directional bias, adults manifested a bias that was consistent with the writing system of their language. These results support the cultural hypothesis regarding the origin of spatial-representational biases.

We consider compact metric graphs with an arbitrary self adjoint realisation of the differential Laplacian. After discussing spectral properties of Laplacians, we prove several versions of trace formulae, relating Laplace spectra to sums over periodic orbits on the graph. This includes trace formulae with, respectively, absolutely and conditionally convergent periodic orbit sums; the convergence depending on properties of the test functions used. We also prove a trace formula for the heat kernel and provide small-t asymptotics for the trace of the heat kernel.

We investigate the Dirac equation in the semiclassical limit → 0. A semiclassical propagator and a trace formula are derived and are shown to be determined by the classical orbits of a relativistic point particle. In addition, two phase factors enter, one of which can be calculated from the Thomas precession of a classical spin transported along the particle orbits. For the second factor we provide an interpretation in terms of dynamical and geometric phases.

In the Dirac theory for the motion of free relativistic electrons, highly oscillatory components appear in the time evolution of physical observables such as position, velocity, and spin angular momentum. This effect is known as zitterbewegung. We present a theoretical analysis of rather different Hamiltonians with gapped and/or spin-split energy spectrum (including the Rashba, Luttinger, and Kane Hamiltonians) that exhibit analogs of zitterbewegung as a common feature. We find that the amplitude of oscillations of the Heisenberg velocity operator v(t) generally equals the uncertainty for a simultaneous measurement of two linearly independent components of v. It is also shown that many features of zitterbewegung are shared by the simple and well-known Landau Hamiltonian describing the dynamics of two-dimensional (2D) electron systems in the presence of a magnetic field perpendicular to the plane. Finally, we also discuss the oscillatory dynamics of 2D electrons arising from the interplay of Rashba spin splitting and a perpendicular magnetic field.

A class of strongly chaotic systems revealing a strange arithmetical structure is discussed whose quantal energy levels exhibit level attraction rather than repulsion. As an example, the nearest-neighbor level spacings for Artin's billiard have been computed in a large energy range. It is shown that the observed violation of universality has its root in the existence of an infinite number of Hermitian operators (Hecke operators) which commute with the Hamiltonian and generate nongeneric correlations in the eigenfunctions.PACS numbers: 05.45.+b, 03.65.-w There seems to be no doubt that the statistical properties of quantal energy spectra and eigenvectors of classically chaotic systems are well described (with respect to their short-range correlations) by the universal laws of random-matrix theory (RMT) [1], originally proposed by Wigner and by Landau and Smorodinsky and fully developed by Dyson for a better understanding of the resonances of compound nuclei. (See Ref.[2] for a collection of the original papers, and Refs. [1,3,4] for recent reviews.) In the simplest case of generic Hamiltonian systems whose classical motion is time-reversal invariant, two universality classes are predicted: All systems with an integrable classical limit fall into one class, and all systems whose classical limit is strongly chaotic iK systems) fall into another class. Consider, e.g., the density distribution Pis) of "unfolded" nearest-neighbor level spacings s. In accordance with the empirical observation that the short-range spectral fluctuations of integrable systems are just those of random numbers, the level spacing distributions for these systems are Poissonian, i.e., ^PoissonOO = e ~\ while those of chaotic systems are the same as for the eigenvalues of large real symmetric random matrices, i.e., of the Gaussian orthogonal ensemble (GOE), which in the case of Pis) is well approximated by Wigner's surmise Pwigner(^) -J nse ~K S /4 . For small spacings, $-*0, the two distributions exhibit the wellknown phenomenon of level attraction [P(s) -\ -s] for classically integrable systems and of level repulsion [Pis)~~ j s] for strongly chaotic systems. It thus appears that the statistical properties of a given quantum system are already determined by its classical limit, depending only upon whether this is chaotic or not.In this Letter we study an interesting class of strongly chaotic systems whose quantal eigenvalues exhibit surprisingly enough level attraction rather than repulsion, and which thus lead to an apparent violation of the universal laws of RMT. We show that these systems reveal a strange arithmetical structure of chaos, which we call arithmetical chaos, that manifests itself in the existence of an infinite number of Hermitian operators commuting with the quantum Hamiltonian, and which are the origin of unexpected correlations in the quantum eigenstates. The existence of such operators could not be anticipated since these systems, having 2 degrees of freedom and being ergodic, possess classically only a single constant of m...

We determine conditions for the quantisation of graphs using the Dirac operator for both two and four component spinors. According to the Bohigas-Giannoni-Schmit conjecture for such systems with time-reversal symmetry the energy level statistics are expected, in the semiclassical limit, to correspond to those of random matrices from the Gaussian symplectic ensemble. This is confirmed by numerical investigation. The scattering matrix used to formulate the quantisation condition is found to be independent of the type of spinor. We derive an exact trace formula for the spectrum and use this to investigate the form factor in the diagonal approximation.