Statistical properties at the spectrum edge of the QCD Dirac operator

The statistical properties of the spectrum of the staggered Dirac operator in an SU(2) lattice gauge theory are analyzed both in the bulk of the spectrum and at the spectrum edge. Two commonly used statistics, the number variance and the spectral rigidity, are investigated. While the spectral fluctuations at the edge are suppressed to the same extent as in the bulk, the spectra are more rigid at the edge. To study this effect, we introduce a microscopic unfolding procedure to separate the variation of the microscopic spectral density from the fluctuations. For the unfolded data, the number variance shows oscillations of the same kind as before unfolding, and the average spectral rigidity becomes larger than the one in the bulk. In addition, the short-range statistics at the origin is studied. The lattice data are compared to predictions of chiral random-matrix theory, and agreement with the chiral Gaussian Symplectic Ensemble is found.Comment: 12 pages, 22 figures, minor typos corrected, version to appear in Euro. Phys. J.

Interdimensional degeneracies for a quantum NN-body system in DD dimensions

Complete spectrum of exact interdimensional degeneracies for a quantum $N$-body system in $D$-dimensions is presented by the method of generalized spherical harmonic polynomials. In an $N$-body system all the states with angular momentum $[\mu+n]$ in $(D-2n)$ dimensions are degenerate where $[\mu]$ and $D$ are given and $n$ is an arbitrary integer if the representation $[\mu+n]$ exists for the SO($D-2n$) group and $D-2n\geq N$. There is an exceptional interdimensional degeneracy for an $N$-body system between the state with zero angular momentum in $D=N-1$ dimensions and the state with zero angular momentum in $D=N+1$ dimensions.Comment: 8 pages, no figure, RevTex, Accepted by EuroPhys.Let

Cosmological constraints on holographic dark energy models under the energy conditions

We study the holographic and agegraphic dark energy models without interaction using the latest observational Hubble parameter data (OHD), the Union2.1 compilation of type Ia supernovae (SNIa), and the energy conditions. Scenarios of dark energy are distinguished by the cut-off of cosmic age, conformal time, and event horizon. The best-fit value of matter density for the three scenarios almost steadily located at $\Omega_{m0}=0.26$ by the joint constraint. For the agegraphic models, they can be recovered to the standard cosmological model when the constant $c$ which presents the fraction of dark energy approaches to infinity. Absence of upper limit of $c$ by the joint constraint demonstrates the recovery possibility. Using the fitted result, we also reconstruct the current equation of state of dark energy at different scenarios, respectively. Employing the model criteria $\chi^2_{\textrm{min}}/dof$, we find that conformal time model is the worst, but they can not be distinguished clearly. Comparing with the observational constraints, we find that SEC is fulfilled at redshift $0.2 \lesssim z \lesssim 0.3$ with $1\sigma$ confidence level. We also find that NEC gives a meaningful constraint for the event horizon cut-off model, especially compared with OHD only. We note that the energy condition maybe could play an important role in the interacting models because of different degeneracy between $\Omega_m$ and constant $c$.Comment: 8 pages, 4 figures, accepted for publication in PR

Ordered GeSi nanorings grown on patterned Si (001) substrates

An easy approach to fabricate ordered pattern using nanosphere lithography and reactive iron etching technology was demonstrated. Long-range ordered GeSi nanorings with 430 nm period were grown on patterned Si (001) substrates by molecular beam epitaxy. The size and shape of rings were closely associated with the size of capped GeSi quantum dots and the Si capping processes. Statistical analysis on the lateral size distribution shows that the high growth temperature and the long-term annealing can improve the uniformity of nanorings