Microcanonical thermostatistics analysis without histograms: cumulative distribution and Bayesian approaches

Microcanonical thermostatistics analysis has become an important tool to reveal essential aspects of phase transitions in complex systems. An efficient way to estimate the microcanonical inverse temperature $\beta(E)$ and the microcanonical entropy $S(E)$ is achieved with the statistical temperature weighted histogram analysis method (ST-WHAM). The strength of this method lies on its flexibility, as it can be used to analyse data produced by algorithms with generalised sampling weights. However, for any sampling weight, ST-WHAM requires the calculation of derivatives of energy histograms $H(E)$, which leads to non-trivial and tedious binning tasks for models with continuous energy spectrum such as those for biomolecular and colloidal systems. Here, we discuss two alternative methods that avoid the need for such energy binning to obtain continuous estimates for $H(E)$ in order to evaluate $\beta(E)$ by using ST-WHAM: (i) a series expansion to estimate probability densities from the empirical cumulative distribution function (CDF), and (ii) a Bayesian approach to model this CDF. Comparison with a simple linear regression method is also carried out. The performance of these approaches is evaluated considering coarse-grained protein models for folding and peptide aggregation.Comment: 9 pages, 11 figure

Speed of light on rotating platforms

It is often taken for granted that on board a rotating disk it is possible to operate a \QTR{it}{global}3+1 splitting of space-time, such that both lengths and time intervals are \QTR{it}{uniquely} defined in terms of measurements performed by real rods and real clocks at rest on the platform. This paper shows that this assumption, although widespread and apparently trivial, leads to an anisotropy of the velocity of two light beams travelling in opposite directions along the rim of the disk; which in turn implies some recently pointed out paradoxical consequences undermining the self-consistency of the Special Theory of Relativity (SRT). A correct application of the SRT solves the problem and recovers complete internal consistency for the theory. As an immediate consequence, it is shown that the Sagnac effect only depends on the non homogeneity of time on the platform and has nothing to do with any anisotropy of the speed of light along the rim of the disk, contrary to an incorrect but widely supported idea.Comment: Latex, 2 figure

Density Matrix Renormalization Group for Dummies

We describe the Density Matrix Renormalization Group algorithms for time dependent and time independent Hamiltonians. This paper is a brief but comprehensive introduction to the subject for anyone willing to enter in the field or write the program source code from scratch.Comment: 29 pages, 9 figures. Published version. An open source version of the code can be found at http://qti.sns.it/dmrg/phome.htm

A continuous population of variable stars up to about 1.5 mag above the horizontal branch?

Increasing samples of pulsating variable stars populating the classical instability strip from the horizontal branch to a few magnitudes brighter are being found in several Local Group galaxies, irrespective of the galaxy morphological type. We will review the observational scenario focusing in particular on the Anomalous Cepheids and related objects.Comment: 5 pages, 2 figures, invited review in JENAM 2003, "Minisymposium: Asteroseismology and Stellar Evolution", Communications in Asteroseismology, in pres

Quantum Interference Effects in Spacetime of Slowly Rotating Compact Objects in Braneworld

The phase shift a neutron interferometer caused by the gravitational field and the rotation of the earth is derived in a unified way from the standpoint of general relativity. General relativistic quantum interference effects in the slowly rotating braneworld as the Sagnac effect and phase shift effect of interfering particle in neutron interferometer are considered. It was found that in the case of the Sagnac effect the influence of brane parameter is becoming important due to the fact that the angular velocity of the locally non rotating observer must be larger than one in the Kerr space-time. In the case of neutron interferometry it is found that due to the presence of the parameter $Q^{*}$ an additional term in the phase shift of interfering particle emerges from the results of the recent experiments we have obtained upper limit for the tidal charge as $Q^{*}\lesssim 10^{7} \rm{cm}^{2}$. Finally, as an example, we apply the obtained results to the calculation of the (ultra-cold neutrons) energy level modification in the braneworld.Comment: 12 pages, 2 figure

Spacetime geometries and light trapping in travelling refractive index perturbations

In the framework of transformation optics, we show that the propagation of a locally superluminal refractive index perturbation (RIP) in a Kerr medium can be described, in the eikonal approximation, by means of a stationary metric, which we prove to be of Gordon type. Under suitable hypotheses on the RIP, we obtain a stationary but not static metric, which is characterized by an ergosphere and by a peculiar behaviour of the geodesics, which are studied numerically, also accounting for material dispersion. Finally, the equation to be satisfied by an event horizon is also displayed and briefly discussed.Comment: 14 pages, 7 figure

A direct kinematical derivation of the relativistic Sagnac effect for light or matter beams

The Sagnac time delay and the corresponding Sagnac phase shift, for relativistic matter and electromagnetic beams counter-propagating in a rotating interferometer, are deduced on the ground of relativistic kinematics. This purely kinematical approach allows to explain the ''universality'' of the effect, namely the fact that the Sagnac time difference does not depend on the physical nature of the interfering beams. The only prime requirement is that the counter-propagating beams have the same velocity with respect to any Einstein synchronized local co-moving inertial frame.Comment: 10 pages, 1 EPS figure, to appear in General Relativity and Gravitatio