On the robustness of q-expectation values and Renyi entropy

We study the robustness of functionals of probability distributions such as the R\'enyi and nonadditive S_q entropies, as well as the q-expectation values under small variations of the distributions. We focus on three important types of distribution functions, namely (i) continuous bounded (ii) discrete with finite number of states, and (iii) discrete with infinite number of states. The physical concept of robustness is contrasted with the mathematically stronger condition of stability and Lesche-stability for functionals. We explicitly demonstrate that, in the case of continuous distributions, once unbounded distributions and those leading to negative entropy are excluded, both Renyi and nonadditive S_q entropies as well as the q-expectation values are robust. For the discrete finite case, the Renyi and nonadditive S_q entropies and the q-expectation values are robust. For the infinite discrete case, where both Renyi entropy and q-expectations are known to violate Lesche-stability and stability respectively, we show that one can nevertheless state conditions which guarantee physical robustness.Comment: 6 pages, to appear in Euro Phys Let

Dark-Halo Cusp: Asymptotic Convergence

We propose a model for how the buildup of dark halos by merging satellites produces a characteristic inner cusp, of a density profile \rho \prop r^-a with a -> a_as > 1, as seen in cosmological N-body simulations of hierarchical clustering scenarios. Dekel, Devor & Hetzroni (2003) argue that a flat core of a<1 exerts tidal compression which prevents local deposit of satellite material; the satellite sinks intact into the halo center thus causing a rapid steepening to a>1. Using merger N-body simulations, we learn that this cusp is stable under a sequence of mergers, and derive a practical tidal mass-transfer recipe in regions where the local slope of the halo profile is a>1. According to this recipe, the ratio of mean densities of halo and initial satellite within the tidal radius equals a given function psi(a), which is significantly smaller than unity (compared to being 1 according to crude resonance criteria) and is a decreasing function of a. This decrease makes the tidal mass transfer relatively more efficient at larger a, which means steepening when a is small and flattening when a is large, thus causing converges to a stable solution. Given this mass-transfer recipe, linear perturbation analysis, supported by toy simulations, shows that a sequence of cosmological mergers with homologous satellites slowly leads to a fixed-point cusp with an asymptotic slope a_as>1. The slope depends only weakly on the fluctuation power spectrum, in agreement with cosmological simulations. During a long interim period the profile has an NFW-like shape, with a cusp of 1<a<a_as. Thus, a cusp is enforced if enough compact satellite remnants make it intact into the inner halo. In order to maintain a flat core, satellites must be disrupted outside the core, possibly as a result of a modest puffing up due to baryonic feedback.Comment: 37 pages, Latex, aastex.cls, revised, ApJ, 588, in pres

Prima Facie Questions in Quantum Gravity

The long history of the study of quantum gravity has thrown up a complex web of ideas and approaches. The aim of this article is to unravel this web a little by analysing some of the {\em prima facie\/} questions that can be asked of almost any approach to quantum gravity and whose answers assist in classifying the different schemes. Particular emphasis is placed on (i) the role of background conceptual and technical structure; (ii) the role of spacetime diffeomorphisms; and (iii) the problem of time.Comment: 20,IC/TP/0

Correlation of pre-earthquake electromagnetic signals with laboratory and field rock experiments

Analysis of the 2007 &lt;i&gt;M&lt;/i&gt;5.4 Alum Rock earthquake near San José California showed that magnetic pulsations were present in large numbers and with significant amplitudes during the 2 week period leading up the event. These pulsations were 1–30 s in duration, had unusual polarities (many with only positive or only negative polarities versus both polarities), and were different than other pulsations observed over 2 years of data in that the pulse sequence was sustained over a 2 week period prior to the quake, and then disappeared shortly after the quake. A search for the underlying physics process that might explain these pulses was was undertaken, and one theory (Freund, 2002) demonstrated that charge carriers were released when various types of rocks were stressed in a laboratory environment. It was also significant that the observed charge carrier generation was transient, and resulted in pulsating current patterns. In an attempt to determine if this phenomenon occurred outside of the laboratory environment, the authors scaled up the physics experiment from a relatively small rock sample in a dry laboratory setting, to a large 7 metric tonne boulder comprised of Yosemite granite. This boulder was located in a natural, humid (above ground) setting at Bass Lake, Ca. The boulder was instrumented with two Zonge Engineering, Model ANT4 induction type magnetometers, two Trifield Air Ion Counters, a surface charge detector, a geophone, a Bruker Model EM27 Fourier Transform Infra Red (FTIR) spectrometer with Sterling cycle cooler, and various temperature sensors. The boulder was stressed over about 8 h using expanding concrete (Bustar&lt;sup&gt;tm&lt;/sup&gt;), until it fractured into three major pieces. The recorded data showed surface charge build up, magnetic pulsations, impulsive air conductivity changes, and acoustical cues starting about 5 h before the boulder actually broke. These magnetic and air conductivity pulse signatures resembled both the laboratory rock stressing results and the 30 October 2007 &lt;i&gt;M&lt;/i&gt;5.4 Alum Rock earthquake field data. &lt;br&gt;&lt;br&gt; The second part of this paper examined other California earthquakes, prior to the Alum Rock earthquake, to see if magnetic pulsations were also present prior to those events. A search for field examples of medium earthquakes was performed to identify earthquakes where functioning magnetometers were present within 20 km, the expected detection range of the magnetometers. Two earthquakes identified in the search included the 12 August 1998 &lt;i&gt;M&lt;/i&gt;5.1 San Juan Bautista (Hollister Ca.) earthquake and the 28 September 2004 &lt;i&gt;M&lt;/i&gt;6.0 Parkfield Ca. earthquake. Both of these data sets were recorded using EMI Corp. Model BF4 induction magnetometers, installed in equipment owned and operated by UC Berkeley. Unfortunately, no air conductivity or IR data were available for these earthquake examples. This new analysis of old data used the raw time series data (40 samples per s), and examined the data for short duration pulsations that exceeded the normal background noise levels at each site, similar to the technique used at Alum Rock. Analysis of Hollister magnetometer, positioned 2 km from the epicenter, showed a significant increase in magnetic pulsations above quiescient threshold levels several weeks prior, and especially 2 days prior to the quake. The pattern of positive and negative pulsations observed at Hollister, were similar, but not identical to Alum Rock in that the pattern of pulsations were interspersed with Pc 1 pulsation trains, and did not start 2 weeks prior to the quake, but rather 2 days prior. The Parkfield data (magnetometer positioned 19 km from the epicenter) showed much smaller pre-earthquake pulsations, but the area had significantly higher conductivity (which attenuates the signals). More interesting was the fact that significant pulsations occurred between the aftershock sequences of quakes as the crustal stress patterns were migrating. &lt;br&gt;&lt;br&gt; Comparing laboratory, field experiments with a boulder, and earthquake events, striking similarities were noted in magnetic pulsations and air conductivity changes, as well as IR signals (where instrumented). More earthquake samples, taken with the appropriate detectors and within 10–15 km proximity to large (&gt;&lt;i&gt;M&lt;/i&gt;5) earthquakes, are still needed to provide more evidence to understand the variability between earthquakes and various electromagnetic signals detected prior to large earthquakes

The Equivalence Principle in the Non-baryonic Regime

We consider the empirical validity of the equivalence principle for non-baryonic matter. Working in the context of the TH\epsilon\mu formalism, we evaluate the constraints experiments place on parameters associated with violation of the equivalence principle (EVPs) over as wide a sector of the standard model as possible. Specific examples include new parameter constraints which arise from torsion balance experiments, gravitational red shift, variation of the fine structure constant, time-dilation measurements, and matter/antimatter experiments. We find several new bounds on EVPs in the leptonic and kaon sectors.Comment: 22 pages, late

Hard Thermal Loops and Chiral Lagrangians

Chiral symmetry is used as the guiding principle to derive hard thermal loop effects in chiral perturbation theory. This is done by using a chiral invariant background field method for the non-linear sigma model and the Wess-Zumino-Witten lagrangian, with and without external vector and axial vector sources. It is then shown that the n-point hard thermal loop is the leading thermal correction for the Green function of n point vector soft quark currents.Comment: 15 pages, Revtex, references added, typos corrected, final version to appear in Phys. Rev.

Harmonic oscillator well with a screened Coulombic core is quasi-exactly solvable

In the quantization scheme which weakens the hermiticity of a Hamiltonian to its mere PT invariance the superposition V(x) = x^2+ Ze^2/x of the harmonic and Coulomb potentials is defined at the purely imaginary effective charges (Ze^2=if) and regularized by a purely imaginary shift of x. This model is quasi-exactly solvable: We show that at each excited, (N+1)-st harmonic-oscillator energy E=2N+3 there exists not only the well known harmonic oscillator bound state (at the vanishing charge f=0) but also a normalizable (N+1)-plet of the further elementary Sturmian eigenstates \psi_n(x) at eigencharges f=f_n > 0, n = 0, 1, ..., N. Beyond the first few smallest multiplicities N we recommend their perturbative construction.Comment: 13 pages, Latex file, to appear in J. Phys. A: Math. Ge

A family of complex potentials with real spectrum

We consider a two-parameter non hermitean quantum-mechanical hamiltonian that is invariant under the combined effects of parity and time reversal transformation. Numerical investigation shows that for some values of the potential parameters the hamiltonian operator supports real eigenvalues and localized eigenfunctions. In contrast with other PT symmetric models, which require special integration paths in the complex plane, our model is integrable along a line parallel to the real axis.Comment: Six figures and four table