59 research outputs found
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 ÎŽ-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 âŒ26 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
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