Amplitude- and Fluctuation-based Dispersion Entropy

Dispersion entropy (DispEn) is a recently introduced entropy metric to quantify the uncertainty of time series. It is fast and, so far, it has demonstrated very good performance in the characterisation of time series. It includes a mapping step, but the effect of different mappings has not been studied yet. Here, we investigate the effect of linear and nonlinear mapping approaches in DispEn. We also inspect the sensitivity of different parameters of DispEn to noise. Moreover, we develop fluctuation-based DispEn (FDispEn) as a measure to deal with only the fluctuations of time series. Furthermore, the original and fluctuation-based forbidden dispersion patterns are introduced to discriminate deterministic from stochastic time series. Finally, we compare the performance of DispEn, FDispEn, permutation entropy, sample entropy, and Lempel–Ziv complexity on two physiological datasets. The results show that DispEn is the most consistent technique to distinguish various dynamics of the biomedical signals. Due to their advantages over existing entropy methods, DispEn and FDispEn are expected to be broadly used for the characterization of a wide variety of real-world time series. The MATLAB codes used in this paper are freely available at http://dx.doi.org/10.7488/ds/2326

Trans-Planckian Issues for Inflationary Cosmology

The accelerated expansion of space during the period of cosmological inflation leads to trans-Planckian issues which need to be addressed. Most importantly, the physical wavelength of fluctuations which are studied at the present time by means of cosmological observations may well originate with a wavelength smaller than the Planck length at the beginning of the inflationary phase. Thus, questions arise as to whether the usual predictions of inflationary cosmology are robust considering our ignorance of physics on trans-Planckian scales, and whether the imprints of Planck-scale physics are at the present time observable. These and other related questions are reviewed in this article.Comment: 32 pages, 11 figures; invited review for "Classical and Quantum Gravity

Cluster formation in asymmetric nuclear matter: semi-classical and quantal approaches

The nuclear-matter liquid-gas phase transition induces instabilities against finite-size density fluctuations. This has implications for both heavy-ion-collision and compact-star physics. In this paper, we study the clusterization properties of nuclear matter in a scenario of spinodal decomposition, comparing three different approaches: the quantal RPA, its semi-classical limit (Vlasov method), and a hydrodynamical framework. The predictions related to clusterization are qualitatively in good agreement varying the approach and the nuclear interaction. Nevertheless, it is shown that i) the quantum effects reduce the instability zone, and disfavor short-wavelength fluctuations; ii) large differences appear bewteen the two semi-classical approaches, which correspond respectively to a collisionless (Vlasov) and local equilibrium description (hydrodynamics); iii) the isospin-distillation effect is stronger in the local equilibrium framework; iv) important variations between the predicted time-scales of cluster formation appear near the borders of the instability region.Comment: 27 pages, 11 figures, Submitted to Nuclear Physics A, Nuclear Physics A In press (2008

Bosons in high temperature superconductors: an experimental survey

We review a number of experimental techniques that are beginning to reveal fine details of the bosonic spectrum \alpha^2F(\Omega) that dominates the interaction between the quasiparticles in high temperature superconductors. Angle-resolved photo emission (ARPES) shows kinks in electronic dispersion curves at characteristic energies that agree with similar structures in the optical conductivity and tunnelling spectra. Each technique has its advantages. ARPES is momentum resolved and offers independent measurements of the real and imaginary part of the contribution of the bosons to the self energy of the quasiparticles. The optical conductivity can be used on a larger variety of materials and with the use of maximum entropy techniques reveals rich details of the spectra including their evolution with temperature and doping. Scanning tunnelling spectroscopy offers spacial resolution on the unit cell level. We find that together the various spectroscopies, including recent Raman results, are pointing to a unified picture of a broad spectrum of bosonic excitations at high temperature which evolves, as the temperature is lowered into a peak in the 30 to 60 meV region and a featureless high frequency background in most of the materials studied. This behaviour is consistent with the spectrum of spin fluctuations as measured by magnetic neutron scattering. However, there is evidence for a phonon contribution to the bosonic spectrum as well.Comment: 71 pages, 52 figure