Evidences of evanescent Bloch waves in Phononic Crystals

We show both experimentally and theoretically the evanescent behaviour of modes in the Band Gap (BG) of finite Phononic Crystal (PC). Based on experimental and numerical data we obtain the imaginary part of the wave vector in good agreement with the complex band structures obtained by the Extended Plane Wave Expansion (EPWE). The calculated and measured acoustic field of a localized mode out of the point defect inside the PC presents also evanescent behaviour. The correct understanding of evanescent modes is fundamental for designing narrow filters and wave guides based on Phononic Crystals with defects.Comment: 8 pages, 3 figure

Real-time evolution of a large-scale relativistic jet

Context. Astrophysical jets are ubiquitous in the Universe on all scales, but their large-scale dynamics and evolution in time are hard to observe since they usually develop at a very slow pace. Aims. We aim to obtain the first observational proof of the expected large-scale evolution and interaction with the environment in an astrophysical jet. Only jets from microquasars offer a chance to witness the real-time, full-jet evolution within a human lifetime, since they combine a 'short', few parsec length with relativistic velocities. Methods. The methodology of this work is based on a systematic recalibraton of interferometric radio observations of microquasars available in public archives. In particular, radio observations of the microquasar GRS 1758-258 over less than two decades have provided the most striking results. Results. Significant morphological variations in the extended jet structure of GRS 1758-258 are reported here that were previously missed. Its northern radio lobe underwent a major morphological variation that rendered the hotspot undetectable in 2001 and reappeared again in the following years. The reported changes confirm the Galactic nature of the source. We tentatively interpret them in terms of the growth of instabilities in the jet flow. There is also evidence of surrounding cocoon. These results can provide a testbed for models accounting for the evolution of jets and their interaction with the environment.Comment: 5 pages, 3 figures, 2 tables. Accepted for publication in Astronomy and Astrophysics Letter

On the structure of the sets of mutually unbiased bases for N qubits

For a system of N qubits, spanning a Hilbert space of dimension d=2^N, it is known that there exists d+1 mutually unbiased bases. Different construction algorithms exist, and it is remarkable that different methods lead to sets of bases with different properties as far as separability is concerned. Here we derive the four sets of nine bases for three qubits, and show how they are unitarily related. We also briefly discuss the four-qubit case, give the entanglement structure of sixteen sets of bases,and show some of them, and their interrelations, as examples. The extension of the method to the general case of N qubits is outlined.Comment: 16 pages, 10 tables, 1 figur

Spatial analysis and site formation processes associated with the Middle Pleistocene hominid teeth from Q1/B waterhole, Boxgrove (West Sussex, UK)

Boxgrove is a key locale for our understanding of Middle Pleistocene human behaviour in Northwestern Europe. It provides high-resolution evidence for behaviour at scale in fine-grained sediments, dating from the end of the MIS13 interglacial at around 480,000 years ago. Excavations at this site in the last quarter of the twentieth century have provided a large body of interdisciplinary data, comprising stone artefact assemblages, well-preserved faunal remains and paleoenvironmental archives, from over 100 test pits and larger excavation areas. The excavation area designated Q1/B was excavated between 1995 and 1996 and provided a particularly deep and complex record of early human activity centred upon a pond or waterhole within the wider landscape. In this work, we present a new analysis of spatial data from a single sedimentary unit (Unit 4u) at the Boxgrove Q1/B site. We consider the spatial disposition of lithic and faunal materials, fabric analysis and the role of the palaeotopography in their distribution. The results indicate that, although the dynamic fluvial depositional environment had an undeniable role in the distribution of materials, the scale and nature of post-depositional movement are consistent with the artefacts being preserved within an autochthonous depositional context, not reworked from an earlier sedimentary unit or subject to long-distance transportation. These results are consistent with previous analysis which suggests that the overall lithic assemblage can be directly compared with others from the wider landscape in compositional terms to interpret the behavioural controls over site formation behind the Q1/B archaeology

Evanescent modes in Sonic Crystals: Complex relation dispersion and supercell approximation

Evanescent modes in complete sonic crystals (SC) and SC with point defects are reported both theoretically and experimentally in this paper. Plane wave expansion (PWE) and, in general, $\omega(k)$ methods have been used to calculate band structures showing gaps that have been interpreted as ranges of frequencies where no real $k$ exists. In this work, we extend PWE to solve the complex $k(\omega)$ problem applied to SC, introducing the supercell approximation for studying one vacancy. Explicit matrix formulation of the equations is given. This $k(\omega)$ method enables the calculation of complex band structures, as well as enabling an analysis of the propagating modes related with real values of the function $k(\omega)$, and the evanescent modes related with imaginary values of $k(\omega)$. This paper shows theoretical results and experimental evidences of the evanescent behavior of modes inside the SC band gap. Experimental data and numerical results using the finite elements method are in very good agreement with the predictions obtained using the $k(\omega)$ method.Comment: 15 pages, 3 figure

Certainty relations between local and nonlocal observables

We demonstrate that for an arbitrary number of identical particles, each defined on a Hilbert-space of arbitrary dimension, there exists a whole ladder of relations of complementarity between local, and every conceivable kind of joint (or nonlocal) measurements. E.g., the more accurate we can know (by a measurement) some joint property of three qubits (projecting the state onto a tripartite entangled state), the less accurate some other property, local to the three qubits, become. We also show that the corresponding complementarity relations are particularly tight for particles defined on prime dimensional Hilbert spaces.Comment: 4 pages, no figure