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 and critical fluctuations at the Anderson transition

Critical fluctuations of wave functions and energy levels at the Anderson transition are studied for the family of the critical power-law random banded matrix ensembles. It is shown that the distribution functions of the inverse participation ratios (IPR) $P_q$ are scale-invariant at the critical point, with a power-law asymptotic tail. The IPR distribution, the multifractal spectrum and the level statistics are calculated analytically in the limits of weak and strong couplings, as well as numerically in the full range of couplings.Comment: 14 pages, 13 eps 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.

Activity-based protein profiling of the human failing ischemic heart reveals alterations in hydrolase activities involving the endocannabinoid system

Acute myocardial infarction and subsequent post-infarction heart failure are among the leading causes of mortality worldwide. The endocannabinoid system has emerged as an important modulator of cardiovascular disease, however the role of endocannabinoid metabolic enzymes in heart failure is still elusive. Herein, we investigated the endocannabinoids and their metabolic enzymes in ischemic end-stage failing human hearts and non-failing controls.\nQuantitative real-time PCR, targeted lipidomics, and activity-based protein profiling (ABPP) enabled assessment of the endocannabinoids and their metabolic enzymes in ischemic end-stage failing human hearts and non-failing controls. Based on lipidomic analysis, two subgroups were identified within the ischemic heart failure group; the first similar to control hearts and the second with decreased levels of the endocannabinoid 2-arachidonoyl-glycerol (2-AG) and drastically increased levels of the endocannabinoid anandamide (AEA), other N-acylethanolamines (NAEs) and free fatty acids. The altered lipid profile was accompanied by strong reductions in the activity of 13 hydrolases, including the 2-AG hydrolytic enzyme monoacylglycerol lipase (MGLL).\nOur findings suggest the presence of different biological states within the ischemic heart failure group, based on alterations in the lipid and hydrolase activity profiles. In addition, this study demonstrates that ABPP is a valuable tool to rapidly analyze enzyme activity in clinical samples with potential for novel drug and biomarker discovery.\nAIM\nMETHODS AND RESULTS\nCONCLUSIONSMolecular Physiolog