Fluctuation of the Correlation Dimension and the Inverse Participation Number at the Anderson Transition

The distribution of the correlation dimension in a power law band random matrix model having critical, i.e. multifractal, eigenstates is numerically investigated. It is shown that their probability distribution function has a fixed point as the system size is varied exactly at a value obtained from the scaling properties of the typical value of the inverse participation number. Therefore the state-to-state fluctuation of the correlation dimension is tightly linked to the scaling properties of the joint probability distribution of the eigenstates.Comment: 4 pages, 5 figure

Critical statistics in a power-law random banded matrix ensemble

We investigate the statistical properties of the eigenvalues and eigenvectors in a random matrix ensemble with $H_{ij}\sim |i-j|^{-\mu}$. It is known that this model shows a localization-delocalization transition (LDT) as a function of the parameter $\mu$. The model is critical at $\mu=1$ and the eigenstates are multifractals. Based on numerical simulations we demonstrate that the spectral statistics at criticality differs from semi-Poisson statistics which is expected to be a general feature of systems exhibiting a LDT or `weak chaos'.Comment: 4 pages in PS including 5 figure

Multifractality of Hamiltonians with power-law transfer terms

Finite-size effects in the generalized fractal dimensions $d_q$ are investigated numerically. We concentrate on a one-dimensional disordered model with long-range random hopping amplitudes in both the strong- and the weak-coupling regime. At the macroscopic limit, a linear dependence of $d_q$ on $q$ is found in both regimes for values of q \alt 4g^{-1}, where $g$ is the coupling constant of the model.Comment: RevTex4, 5 two-column pages, 5 .eps figures, to be published in Phys. Rev.

f(α)f(\alpha) Multifractal spectrum at strong and weak disorder

The system size dependence of the multifractal spectrum $f(\alpha)$ and its singularity strength $\alpha$ is investigated numerically. We focus on one-dimensional (1D) and 2D disordered systems with long-range random hopping amplitudes in both the strong and the weak disorder regime. At the macroscopic limit, it is shown that $f(\alpha)$ is parabolic in the weak disorder regime. In the case of strong disorder, on the other hand, $f(\alpha)$ strongly deviates from parabolicity. Within our numerical uncertainties it has been found that all corrections to the parabolic form vanish at some finite value of the coupling strength.Comment: RevTex4, 6 two-column pages, 4 .eps figures, new results added, updated references, to be published in Phys. Rev.

Technical Design Report for the Panda Forward Spectrometer Calorimeter

This document is devoted to the electromagnetic calorimeter of the Forward Spectrometer and describes the design considerations, the technical layout, the expected performance, and the production readiness

Experimental access to Transition Distribution Amplitudes with the P̄ANDA experiment at FAIR

Baryon-to-meson Transition Distribution Amplitudes (TDAs) encoding valuable new information on hadron structure appear as building blocks in the collinear factorized description for several types of hard exclusive reactions. In this paper, we address the possibility of accessing nucleon-to-pion (\u3c0N) TDAs from \uafpp \u2192 e+e 12\u3c00 reaction with the future PANDA detector at the FAIR facility. At high center- of-mass energy and high invariant mass squared of the lepton pair q2, the amplitude of the signal channel pp\uaf \u2192 e+e 12\u3c00 admits a QCD factorized description in terms of \u3c0N TDAs and nucleon Distribution Amplitudes (DAs) in the forward and backward kinematic regimes. Assuming the validity of this factorized description, we perform feasibility studies for measuring \uafpp \u2192 e+e 12\u3c00 with the PANDA detector. Detailed simulations on signal reconstruction efficiency as well as on rejection of the most severe background channel, i.e. pp\uaf \u2192 \u3c0+\u3c0 12\u3c00 were performed for the center-of-mass energy squared s = 5 GeV2 and s = 10 GeV2, in the kinematic regions 3.0 0.5 in the proton-antiproton center-of-mass frame. Results of the simulation show that the particle identification capabilities of the PANDA detector will allow to achieve a background rejection factor of 5 \ub7 107 (1 \ub7 107) at low (high) q2 for s = 5 GeV2, and of 1 \ub7 108 (6 \ub7 106) at low (high) q2 for s = 10 GeV2, while keeping the signal reconstruction efficiency at around 40%. At both energies, a clean lepton signal can be reconstructed with the expected statistics corresponding to 2 fb 121 of integrated luminosity. The cross sections obtained from the simulations are used to show that a test of QCD collinear factorization can be done at the lowest order by measuring scaling laws and angular distributions. The future measurement of the signal channel cross section with PANDA will provide a new test of the perturbative QCD description of a novel class of hard exclusive reactions and will open the possibility of experimentally accessing \u3c0N TDAs

Technical Design Report for the Panda Forward Spectrometer Calorimeter

This document is devoted to the electromagnetic calorimeter of the Forward Spectrometer and describes the design considerations, the technical layout, the expected performance, and the production readiness