Integro-differential diffusion equation for continuous time random walk

In this paper we present an integro-differential diffusion equation for continuous time random walk that is valid for a generic waiting time probability density function. Using this equation we also study diffusion behaviors for a couple of specific waiting time probability density functions such as exponential, and a combination of power law and generalized Mittag-Leffler function. We show that for the case of the exponential waiting time probability density function a normal diffusion is generated and the probability density function is Gaussian distribution. In the case of the combination of a power-law and generalized Mittag-Leffler waiting probability density function we obtain the subdiffusive behavior for all the time regions from small to large times, and probability density function is non-Gaussian distribution.Comment: 12 page

Narrative coherence in multiple forensic interviews with child witnesses alleging physical and sexual abuse

This study investigated the narrative coherence of children's accounts elicited in multiple forensic interviews. Transcriptions of 56 police interviews with 28 children aged 3–14 years alleging physical and sexual abuse were coded for markers of completeness, consistency and connectedness. We found that multiple interviews increased the completeness of children's testimony, containing on average almost twice as much new information as single interviews, including crucial location, time and abuse‐related details. When both contradictions within the same interview and across interviews were considered, contradictions were not more frequent in multiple interviews. The frequency of linguistic markers of connectedness remained stable across interviews. Multiple interviews increase the narrative coherence of children's testimony through increasing their completeness without necessarily introducing contradictions or decreasing causal‐temporal connections between details. However, as ‘ground truth’ is not known in field studies, further investigation of the relationship between the narrative coherence and accuracy of testimonies is required

Complementarity in generic open quantum systems

We develop a unified, information theoretic interpretation of the number-phase complementarity that is applicable both to finite-dimensional (atomic) and infinite-dimensional (oscillator) systems, with number treated as a discrete Hermitian observable and phase as a continuous positive operator valued measure (POVM). The relevant uncertainty principle is obtained as a lower bound on {\it entropy excess}, $X$, the difference between the entropy of one variable, typically the number, and the knowledge of its complementary variable, typically the phase, where knowledge of a variable is defined as its relative entropy with respect to the uniform distribution. In the case of finite dimensional systems, a weighting of phase knowledge by a factor $\mu$ ($> 1$) is necessary in order to make the bound tight, essentially on account of the POVM nature of phase as defined here. Numerical and analytical evidence suggests that $\mu$ tends to 1 as system dimension becomes infinite. We study the effect of non-dissipative and dissipative noise on these complementary variables for oscillator as well as atomic systems.Comment: 18 pages, 15 figures; accepted for publication in Modern Physics Letters

Counting statistics of tunneling through a single molecule: effect of distortion and displacement of vibrational potential surface

We analyze the effects of a distortion of the nuclear potential of a molecular quantum dot (QD), as well as a shift of its equilibrium position, on nonequilibrium-vibration-assisted tunneling through the QD with a single level ($\epsilon_d$) coupled to the vibrational mode. For this purpose, we derive an explicit analytical expression for the Franck-Condon (FC) factor for a displaced-distorted oscillator surface of the molecule and establish rate equations in the joint electron-phonon representation to examine the current-voltage characteristics and zero-frequency shot noise, and skewness as well. Our numerical analyses shows that the distortion has two important effects. The first one is that it breaks the symmetry between the excitation spectra of the charge states, leading to asymmetric tunneling properties with respect to $\epsilon_d>0$ and $\epsilon_d<0$. Secondly, distortion (frequency change of the oscillator) significantly changes the voltage-activated cascaded transition mechanism, and consequently gives rise to a different nonequilibrium vibrational distribution from that of the case without distortion. Taken in conjunction with strongly modified FC factors due to distortion, this results in some new transport features: the appearance of strong NDC even for a single-level QD with symmetric tunnel couplings; a giant Fano factor even for a molecule with an extremely weak electron-phonon interaction; and enhanced skewness that can have a large negative value under certain conditions.Comment: 29 pages, 11 figures, published versio

Brownian Motion and Polymer Statistics on Certain Curved Manifolds

We have calculated the probability distribution function G(R,L|R',0) of the end-to-end vector R-R' and the mean-square end-to-end distance (R-R')^2 of a Gaussian polymer chain embedded on a sphere S^(D-1) in D dimensions and on a cylinder, a cone and a curved torus in 3-D. We showed that: surface curvature induces a geometrical localization area; at short length the polymer is locally "flat" and (R-R')^2 = L l in all cases; at large scales, (R-R')^2 is constant for the sphere, it is linear in L for the cylinder and reaches different constant values for the torus. The cone vertex induces (function of opening angle and R') contraction of the chain for all lengths. Explicit crossover formulas are derived.Comment: 9 pages, 4 figures, RevTex, uses amssymb.sty and multicol.sty, to appear in Phys. Rev

Static interactions and stability of matter in Rindler space

Dynamical issues associated with quantum fields in Rindler space are addressed in a study of the interaction between two sources at rest generated by the exchange of scalar particles, photons and gravitons. These static interaction energies in Rindler space are shown to be scale invariant, complex quantities. The imaginary part will be seen to have its quantum mechanical origin in the presence of an infinity of zero modes in uniformly accelerated frames which in turn are related to the radiation observed in inertial frames. The impact of a uniform acceleration on the stability of matter and the properties of particles is discussed and estimates are presented of the instability of hydrogen atoms when approaching the horizon.Comment: 28 pages, 4 figure

Spectra and Symmetry in Nuclear Pairing

We apply the algebraic Bethe ansatz technique to the nuclear pairing problem with orbit dependent coupling constants and degenerate single particle energy levels. We find the exact energies and eigenstates. We show that for a given shell, there are degeneracies between the states corresponding to less and more than half full shell. We also provide a technique to solve the equations of Bethe ansatz.Comment: 15 pages of REVTEX with 2 eps figure

The decay b -> s g at NLL in the Standard Model

I present the Standard Model calculation of the decay rate for b -> s g (g denotes a gluon) at next-to-leading logarithms (NLL). In order to get a meaningful physical result, the decay b -> s g g and certain contributions of b -> s \bar{f} f (where f are the light quark flavours u, d and s) have to be included as well. Numerically we get BR^(NLL) = (5.0 +/- 1.0) * 10^{-3} which is more than a factor 2 larger than the leading logarithmic result BR^(LL) = (2.2 +/- 0.8) * 10^{-3}. Further, I consider the impact of this contribution on the charmless hadronic branching ratio BRc, which could be used to extract the CKM-ratio |V_(ub)/V_(cb)| with more accuracy. Finally, I have a short look at BRc in scenarios where the Wilson coefficient C_8 is enhanced by new physics.Comment: 7 pages including 5 postscript figures; uses epsfi

Infrared renormalons and single meson production in proton-proton collisions

In this article, we investigate the contribution of the higher twist Feynman diagrams to the large-$p_T$ inclusive pion production cross section in proton-proton collisions and present the general formulae for the higher twist differential cross sections in the case of the running coupling and frozen coupling approaches. The structure of infrared renormalon singularities of the higher twist subprocess cross section and the resummed expression (the Borel sum) for it are found. We compared the resummed higher twist cross sections with the ones obtained in the framework of the frozen coupling approximation and leading twist cross section. We obtain, that ratio $R$ for all values of the transverse momentum $p_{T}$ of the pion identical equivalent to ratio $r$. It is shown that the resummed result depends on the choice of the meson wave functions used in calculation. Phenomenological effects of the obtained results are discussed.Comment: 28 pages, 13 figure

Acausality in Gowdy spacetimes

We present a parametrization of $T^3$ and $S^1\times S^2$ Gowdy cosmological models which allows us to study both types of topologies simultaneously. We show that there exists a coordinate system in which the general solution of the linear polarized special case (with both topologies) has exactly the same functional dependence. This unified parametrization is used to investigate the existence of Cauchy horizons at the cosmological singularities, leading to a violation of the strong cosmic censorship conjecture. Our results indicate that the only acausal spacetimes are described by the Kantowski-Sachs and the Kerr-Gowdy metrics.Comment: Typos corrected, 10 pages. Dedicated to Michael P. Ryan on the occasion of his 60-th birthda