Fake symmetry transitions in lattice Dirac spectra

In a recent lattice investigation of Ginsparg-Wilson-type Dirac operators in the Schwinger model, it was found that the symmetry class of the random matrix theory describing the small Dirac eigenvalues appeared to change from the unitary to the symplectic case as a function of lattice size and coupling constant. We present a natural explanation for this observation in the framework of a random matrix model, showing that the apparent change is caused by the onset of chiral symmetry restoration in a finite volume. A transition from unitary to symplectic symmetry does not occur.Comment: 6 pages, 3 figures, REVTe

Small eigenvalues of the SU(3) Dirac operator on the lattice and in Random Matrix Theory

We have calculated complete spectra of the staggered Dirac operator on the lattice in quenched SU(3) gauge theory for \beta = 5.4 and various lattice sizes. The microscopic spectral density, the distribution of the smallest eigenvalue, and the two-point spectral correlation function are analyzed. We find the expected agreement of the lattice data with universal predictions of the chiral unitary ensemble of random matrix theory up to a certain energy scale, the Thouless energy. The deviations from the universal predictions are determined using the disconnected scalar susceptibility. We find that the Thouless energy scales with the lattice size as expected from theoretical arguments making use of the Gell-Mann--Oakes--Renner relation.Comment: REVTeX, 5 pages, 4 figure

Smallest Dirac Eigenvalue Distribution from Random Matrix Theory

We derive the hole probability and the distribution of the smallest eigenvalue of chiral hermitian random matrices corresponding to Dirac operators coupled to massive quarks in QCD. They are expressed in terms of the QCD partition function in the mesoscopic regime. Their universality is explicitly related to that of the microscopic massive Bessel kernel.Comment: 4 pages, 1 figure, REVTeX. Minor typos in subscripts corrected. Version to appear in Phys. Rev.

Statistical analysis and the equivalent of a Thouless energy in lattice QCD Dirac spectra

Random Matrix Theory (RMT) is a powerful statistical tool to model spectral fluctuations. This approach has also found fruitful application in Quantum Chromodynamics (QCD). Importantly, RMT provides very efficient means to separate different scales in the spectral fluctuations. We try to identify the equivalent of a Thouless energy in complete spectra of the QCD Dirac operator for staggered fermions from SU(2) lattice gauge theory for different lattice size and gauge couplings. In disordered systems, the Thouless energy sets the universal scale for which RMT applies. This relates to recent theoretical studies which suggest a strong analogy between QCD and disordered systems. The wealth of data allows us to analyze several statistical measures in the bulk of the spectrum with high quality. We find deviations which allows us to give an estimate for this universal scale. Other deviations than these are seen whose possible origin is discussed. Moreover, we work out higher order correlators as well, in particular three--point correlation functions.Comment: 24 pages, 24 figures, all included except one figure, missing eps file available at http://pluto.mpi-hd.mpg.de/~wilke/diff3.eps.gz, revised version, to appear in PRD, minor modifications and corrected typos, Fig.4 revise

Predicting evolution and visualizing high-dimensional fitness landscapes

The tempo and mode of an adaptive process is strongly determined by the structure of the fitness landscape that underlies it. In order to be able to predict evolutionary outcomes (even on the short term), we must know more about the nature of realistic fitness landscapes than we do today. For example, in order to know whether evolution is predominantly taking paths that move upwards in fitness and along neutral ridges, or else entails a significant number of valley crossings, we need to be able to visualize these landscapes: we must determine whether there are peaks in the landscape, where these peaks are located with respect to one another, and whether evolutionary paths can connect them. This is a difficult task because genetic fitness landscapes (as opposed to those based on traits) are high-dimensional, and tools for visualizing such landscapes are lacking. In this contribution, we focus on the predictability of evolution on rugged genetic fitness landscapes, and determine that peaks in such landscapes are highly clustered: high peaks are predominantly close to other high peaks. As a consequence, the valleys separating such peaks are shallow and narrow, such that evolutionary trajectories towards the highest peak in the landscape can be achieved via a series of valley crossingsComment: 12 pages, 7 figures. To appear in "Recent Advances in the Theory and Application of Fitness Landscapes" (A. Engelbrecht and H. Richter, eds.). Springer Series in Emergence, Complexity, and Computation, 201

Massive chiral random matrix ensembles at beta = 1 & 4 : Finite-volume QCD partition functions

In a deep-infrared (ergodic) regime, QCD coupled to massive pseudoreal and real quarks are described by chiral orthogonal and symplectic ensembles of random matrices. Using this correspondence, general expressions for the QCD partition functions are derived in terms of microscopically rescaled mass variables. In limited cases, correlation functions of Dirac eigenvalues and distributions of the smallest Dirac eigenvalue are given as ratios of these partition functions. When all masses are degenerate, our results reproduce the known expressions for the partition functions of zero-dimensional sigma models.Comment: 6 pages, REVTeX 3.1, no figure; (v2) corrected signatures of c'

Crossover from strong to weak confinement for excitons in shallow or narrow quantum wells

We present a theoretical study of the crossover from the two-dimensional (2D, separate confinement of the carriers) to the three-dimensional (3D, center-of-mass confinement) behavior of excitons in shallow or narrow quantum wells (QW's). Exciton binding energies and oscillator strengths are calculated by diagonalizing the Hamiltonian on a large nonorthogonal basis set. We prove that the oscillator strength per unit area has a minimum at the crossover, in analogy with the similar phenomenon occurring for the QW to thin-film crossover on increasing the well thickness, and in agreement with the analytic results of a simplified δ-potential model. Numerical results are obtained for GaAs/Alx Ga1-xAs and InxGa1-xAs/GaAs systems. Our approach can also be applied to obtain an accurate description of excitons in QW's with arbitrary values of the offsets (positive or negative) and also for very narrow wells. In particular, the crossover from 2D to 3D behavior in narrow GaAs/AlxGa1-xAs QW's is investigated: the maximum binding energy of the direct exciton in GaAs/AlAs QW's is found to be ∼26 meV and to occur between one and two monolayers

Heterogeneous clinical phenotypes and cerebral malformations reflected by rotatin cellular dynamics

Recessive mutations in RTTN, encoding the protein rotatin, were originally identified as cause of polymicrogyria, a cortical malformation. With time, a wide variety of other brain malformations has been ascribed to RTTN mutations, including primary microcephaly. Rotatin is a centrosomal protein possibly involved in centriolar elongation and ciliogenesis. However, the function of rotatin in brain development is largely unknown and the molecular disease mechanism underlying cortical malformations has not yet been elucidated. We performed both clinical and cell biological studies, aimed at clarifying rotatin function and pathogenesis. Review of the 23 published and five unpublished clinical cases and genomic mutations, including the effect of novel deep intronic pathogenic mutations on RTTN transcripts, allowed us to extrapolate the core phenotype, consisting of intellectual disability, short stature, microcephaly, lissencephaly, periventricular heterotopia, polymicrogyria and other malformations. We show that the severity of the phenotype is related to residual function of the protein, not only the level of mRNA expression. Skin fibroblasts from eight affected individuals were studied by high resolution immunomicroscopy and flow cytometry, in parallel with in vitro expression of RTTN in HEK293T cells. We demonstrate that rotatin regulates different phases of the cell cycle and is mislocalized in affected individuals. Mutant cells showed consistent and severe mitotic failure with centrosome amplification and multipolar spindle formation, leading to aneuploidy and apoptosis, which could relate to depletion of neuronal progenitors often observed in microcephaly. We confirmed the role of rotatin in functional and structural maintenance of primary cilia and determined that the protein localized not only to the basal body, but also to the axoneme, proving the functional interconnectivity between ciliogenesis and cell cycle progression. Proteomics analysis of both native and exogenous rotatin uncovered that rotatin interacts with the neuronal (non-muscle) myosin heavy chain subunits, motors of nucleokinesis during neuronal migration, and in human induced pluripotent stem cell-derived bipolar mature neurons rotatin localizes at the centrosome in the leading edge. This illustrates the role of rotatin in neuronal migration. These different functions of rotatin explain why RTTN mutations can lead to heterogeneous cerebral malformations, both related to proliferation and migration defects.Genetics of disease, diagnosis and treatmen