Using XMM-Newton observations, we investigate the scaling and structural properties of the ICM entropy in a sample of 10 nearby (z < 0.2) relaxed galaxy clusters in the temperature range 2-9 keV. We derive the local entropy-temperature (S –T ) relation at R = 0.1, 0.2, 0.3 and 0.5R200. The logarithmic slope of the relation is the same within the 1σ error at all scaled radii. However, the intrin...

Dispersion-relation methods are used to derive a form-factor representation for the retarded dispersion energy of two hydrogen atoms that are described by relativistic electron theory. By expressing the electromagnetic form factors in terms of atomic transition matrix elements the complete multipole expansion of the interatomic dispersion energy is obtained. The long-range asymptotic limit of t...

We consider the nature of quantum properties in non-relativistic quantum mechanics (QM) and relativistic quantum field theories, and examine the connection between formal quantization schemes and intuitive notions of wave-particle duality. Based on the map between classical Poisson brackets and their associated commutators, such schemes give rise to quantum states obeying canonical dispersion r...

In this study, we consider the propagation of the Love-type wave in piezoelectric gradient covering layer on an elastic half-space having an imperfect interface between them. Dispersion relation has been obtained in the form of determinant for both electrically open and short cases. The effects of different material gradient coefficients of functionally graded piezoelectric material (FGPM) and ...

The free photon dispersion relation is a reference quantity for high precision tests of Lorentz Invariance. We first outline effective approaches to a conceivable Lorentz Invariance Violation (LIV). Next we address phenomenological tests based on the propagation of cosmic rays, in particular in Gamma Ray Bursts (GRBs). As a specific concept, which could imply LIV, we then focus on field theory ...

Hyperasymptotic summation of steepest-descent asymptotic expansions of integrals is extended to functions that satisfy a dispersion relation. We apply the method to energy eigenvalues of the anharmonic oscillator, for which there is no known integral representation, but for which there is a dispersion relation. Hyperasymptotic summation exploits the rich analytic structure underlying the asympt...

We perform a quasinormal mode analysis of black-hole configurations in Bose-Einstein condensates (BECs). In this analysis we use the full Bogoliubov dispersion relation, not just the hydrodynamic or geometric approximation. We restrict our attention to one-dimensional flows in BECs with steplike discontinuities. For this case we show that in the hydrodynamic approximation quasinormal modes do n...

The numerical dispersion relation that governs the propagation of fields in a finite-difference time-domain (FDTD) grid was derived several years ago. In this letter a different interpretation is given for the governing equation. It is shown that the dispersion relation predicts faster-than-light propagation for coarsely resolved fields. Additionally, some spectral components that were previous...

Measurements of the dispersion relation for shear Alfvén waves as a function of perpendicular wave number are reported for the inertial regime for which V{A}>V{Te}. The parallel phase velocity and damping are determined as k{ perpendicular} varies and the measurements are compared to theoretical predictions. The comparison shows that the best agreement between theory and experiment is achieved ...