No abstract

No abstract

No abstract

Two results support the idea that the scalar and vector potentials in the Lorenz gauge can be considered to be physical quantities: (i) they separately satisfy the properties of causality and propagation at the speed of light and not imply spurious terms and (ii) they can naturally be written in a manifestly covariant form. In this paper we introduce expressions for the Lorenzgauge potentials at the present time in terms of electric and magnetic fields at the retarded time.These expressions provide a third result in favor of a physical interpretation of the Lorenz-gauge potentials: (iii) they can be regarded as causal effects of the observed electric and magnetic fields.

No abstract

Fractional cosmology modifies the standard derivative to Caputo’s fractional derivative of order μ, generating changes in General Relativity. Friedmann equations are modified, and the evolution of the species densities depends on μ and the age of the Universe tU. We estimate stringent constraints on μ using cosmic chronometers, Type Ia supernovae, and joint analysis. We obtain $\mu =2.839^{+0.117}_{-0.193}$ within the 1σ confidence level providing a non-standard cosmic acceleration at late times; consequently, the Universe would be older than the standard estimations. Additionally, we present a stability analysis for different μ values. This analysis identifies a late-time attractor corresponding to a power-law decelerated solution for μ < 2. Moreover, a non-relativistic critical point exists for μ > 1 and a sink for μ > 2. This solution is a decelerated power-law if 1 < μ < 2 and an accelerated power-law solution if μ > 2, consistent with the mean values obtained from the observational analysis. Therefore, for both flat FLRW and Bianchi I metrics, the modified Friedmann equations provide a late cosmic acceleration under this paradigm without introducing a dark energy component. This approach could be a new path to tackling unsolved cosmological problems.

Non-linear eigenvalue equations straightforwardly determine fundamental physical quantities of a wide variety of areas. We retrieve a root-locus-like procedure, as a new technique for directly analyzing specific physical phenomena involving multiband-multichannel charge-carrier coupled modes. A new explicit necessary and sufficient condition is presented for a generalized eigenvalue problem, associated with an N -coupled components matrix boundary equation. Within our approach, the uncoupled-system case is nicely recovered. We tested the present scheme by applying it to heavy and light holes, described via the Kohn-Lüttinger model, and found good agreement for our proposition even at medium-intensity band mixing. We simulated the multiband-hole band-mixing-phenomenon by monitoring the root-locus for the quadratic eigenvalue problem, and by plotting the metamorphosis of the effective band offset profile, for bulk and layered heterostructures, respectively. Several new features have been observed; for example, for light holes solely, an appealing interchange of quantum-well-like versus barrier-like roles has been detected for several III-V semiconductor binary compounds.

No abstract