Defining subsystems in Hilbert spaces with non-Euclidean metric

This work outlines a consistent method of identifying subsystems in finite-dimensional Hilbert spaces, independent of the underlying inner-product structure. It has been well established that Hilbert spaces with modified inner-product, defined through the so-called metric operator, turn out to be the most natural ways to represent certain phenomena such as those involving balanced gain and loss resulting in pseudo-Hermitian Hamiltonians. For composite systems undergoing pseudo-Hermitian evolution, defining the subsystems is generally considered feasible only when the metric operator is chosen to have a tensor product form so that a partial trace operation can be well defined. In this work, we use arguments from algebraic quantum mechanics to show that the subsystems can be well-defined in every metric space -- irrespective of whether or not the metric is of tensor product form. This is done by identifying subsystems with a decomposition of the underlying $C^*$-algebra into commuting sub-algebras. We show that different subsystem decompositions correspond to choosing different equivalence classes of the GNS representation. Furthermore, given a form of pseudo-Hermitian Hamiltonian, the choice of the Hamiltonian compatible metric characterizes the subsystem decomposition and as a consequence, the entanglement structure in the system. We clarify how each of the subsystems, defined this way, can be tomographically constructed and that these subsystems satisfy the no-signaling principle. With these results, we put all the choices of the metric operator on an equal footing.Comment: 10 pages, 1 figure, Important revision

Improvement in quantum communication using quantum switch

Applications of the quantum switch on quantum channels have recently become a topic of intense discussion. In the present work, we show that some useless (for communication) channels may provide useful communication under the action of quantum switch for several information-theoretic tasks: quantum random access codes, quantum steering, etc. We demonstrate that the quantum switch can also be useful in preventing the loss of coherence in a system when only coherence-breaking channels are the available channels for communication. We also show that if a useless quantum channel does not provide useful communication even after using a quantum switch, concatenating the channel with another suitable quantum channel, and subsequently using the switch, one may achieve useful communication. Finally, we discuss how the introduction of noise in the quantum switch can reduce the advantage that the switch provides.Comment: 14 pages, 13 figures, comments are welcome. The latest version has an improved presentation of the main result

Reduced dynamics of a PT-symmetric evolution

Evolutions under non-Hermitian Hamiltonians with unbroken PT-symmetry can be considered unitary under appropriate choices of inner products, facilitated by the so-called metric operator. While it is understood that the choice of the metric operator has no bearing on the description of the system, in this work we show that this choice does dictate the properties of the subsystem. Subsystem dynamics therefore does depend on the choice of the metric. We argue that this result is a reformulation of the previously known result that the set of observables, chosen to characterize the state, determines its decomposition into subsystems. In this work we take a non-Hermitian PT-symmetric quantum walk with an internal and external degree of freedom to show this. The Hamiltonian of the quantum walk is chosen to not allow a metric operator with a tensor product structure over these subspaces. Under these constraints, we investigate the properties of the internal state of the system under different choices of the metric operator and show that properties like bipartite entanglement and non-Markovianity depend on the choice of the metric operator.Comment: 16 pages, 5 figures; Comments are welcom

Gravitationally induced entanglement between two quantum walkers

Quantum walk is a synonym for multi-path interference and spread of particle in superposition of position space. We study the effects of a quantum mechanical interaction modeled to mimic quantum mechanical gravitational interaction between the two states of the walkers. The study has been carried out to investigate the entanglement generation between the two quantum walkers that do not otherwise interact. We see that the states do in fact get entangled more and more as the quantum walks unfold. We investigate the dependence of this entanglement generation on the coin parameter of the walks. With the introduction of noise into the dynamics, we also show the sensitivity of entanglement entropy between the two walkers on the noise introduced in one of the walks.Comment: 7 pages, 9 figures, updated version with effect of noise and supplementary informatio

The last glacial maximum Balearic Abyssal Plain megabed revisited

Megabeds are thick sedimentary layers extending over thousands square kilometres in deep sea basins and are thought to result from large slope failures triggered by major external events. Such deposits have been found in at least three areas of the Mediterranean Sea. Although their discovery dates back to the early 1980s, many questions remain, concerning their initiation, source area, extent, and the nature of their emplacement. One of the largest previously documented megabeds was emplaced during the Last Glacial Maximum across the Balearic Abyssal Plain with a thickness of 8-10 m in water depths of up to 2800 m. New 3.5 kHz sub-bottom profiles and sediment cores provide greater constraint on the lateral variability of the megabed and allow to map it beyond previous estimates, with a revised areal extent up to 90,000-100,000 km2. Megabed terminations show gradual pinch-out to the West and an abrupt eastward termination against the Sardinia steep margin. The megabed presents both in seismic profiles and in sediment cores a tripartite subdivision likely corresponding to changes in flow regimes across the basin with a central area of sandy facies and erosional base oriented NNE-SSW allowing renewed discussions about sources and trigger of the megabed

Biochemical profile and in vitro neuroprotective properties of Carpobrotus edulis L., a medicinal and edible halophyte native to the coast of South Africa

This work reports the nutritional profile and in vitro neuroprotective properties of leaves of Carpobrotus edulis L, a medicinal and edible succulent species native to the coast of South Africa. Biomass was evaluated for proximate composition and for contents in carotenoids, liposoluble pigments and minerals. Hexane, dichloromethane, ethyl acetate and methanol extracts were prepared by Soxhlet extraction from dried biomass and evaluated for in vitro inhibition of acetylcholinesterase (AChE) and butyrylcholinesterase (BuChE), capacity to attenuate hydrogen peroxide (H2O2)-induced injury in the human dopaminergic cell line SH-SY5Y and for anti-neuroinflammatory potential on lipopolysaccharide (LPS)-stimulated microglia cells. Extracts were evaluated for antioxidant activity by four complementary methods, total content of phenolics, tannins and flavonoids. Finally the profile of the main phenolic compounds was determined by high performance liquid chromatography with diode array detection (HPLC-DAD). C edulis has a high moisture content, high levels of crude protein, fibre, ash, carotenoids, calcium and iron and a low fat level. The extracts were able to efficiently scavenge the free radical 2,2-diphenyl-1-picrylhydrazyl (DPPH), reduce iron and chelate copper and iron ions, and exhibited different levels of phenolic compounds in the order ethyl acetate > methanol > dichloromethane > hexane. The main compounds detected were gallic and salicylic acids and quercetin, all in the ethyl acetate extract. The extracts allowed a dual and potent inhibition of AChE and BuChE. The dichloromethane and methanol extracts had the strongest capacity to prevent cell death induced by H2O2, and the methanol extract had anti-neuronflammatory properties. All together our results suggest that consumption of leaves of C edulis can contribute for a balanced diet, and that they may add to the improvement of cognitive functions. It also suggests possible novel biotechnological applications of C. edulis such as source of molecules and/or products for the food and/or pharmaceutical industries. Studies aiming to the isolation and identification of the bioactive compounds are already in progress. (C) 2017 SAAB. Published by Elsevier B.V. All rights reserved.Portuguese National BudgetXtremeGourmet project [ALG-01-0247-FEDER-017676]FCT Investigator Programme [IF/00049/2012]info:eu-repo/semantics/publishedVersio

Terminal chop: New technique for full thickness nuclear segmentation in mature hard cataract

We describe an efficient technique, “Terminal Chop,” for full thickness nuclear segmentation in mature hard cataracts. Terminal chop utilizes the principle of secondary rock breakage system with stress concentration to break these hard nuclei. In this technique consonant to drag picks, a specially designed chopper “Terminator” is used to initiate a unique dispersive mechanical force to create a full thickness nuclear crack (crack formation) at the weakest soft and thin equator, which automatically traverses through the center and to the equator on the other side. Lateral separation of both the instruments placed at the equator, propagates the initial full thickness nuclear crack (crack propagation), breaking the entire nucleus into two complete pieces including the posterior plate. The direction of splitting follows the cleavage plane in a more direct manner, thus requiring least fracture force, least manipulation and stress, much lower than compressive stress, causing minimal trauma, and highly satisfactory postoperative results

Seafloor instabilities in the Gulf of Lions, Western Mediterranean

Le golfe du Lion (GoL) est une marge passive d'environ 200 km de long et 70 km de large qui s'étend d’ouest en est du sud de la côte française jusqu’à la plaine abyssale des Baléares (BAP) dans la Méditerranée occidentale. Le talus du golfe du Lion est découpé par quinze canyons sous-marins, le plus grand étant le canyon du Petit Rhône qui canalise les sédiments apportés par le fleuve Rhône à travers le delta du Rhône. Les déstabilisations des fonds marins dans le GoL se produisent à l’embouchure et le long des flancs des canyons, mais aussi dans les zones de pente d'interfluve et les levées des principales vallées sous-marines. Cette thèse de doctorat vise à comprendre les processus de mise en place des trois plus grands dépôts d’accumulation en masse du GoL : ceux du Rhône occidental, du Rhône oriental et de la mégaturbidite de la plaine abyssale des Baléares. J’utilise un nouvel ensemble multidisciplinaire de données comprenant des données géophysiques, sédimentologiques, géotechniques in-situ et de laboratoire. La zone d'étude est caractérisée par de multiples escarpements de glissements. La morphologie des glissements est contrôlée par la présence de plusieurs failles listriques enracinées dans les couches messiniennes. La très haute résolution des données géophysiques nouvellement acquises, entre autre avec des engins tractés près du fond, montre la structure interne des glissements avec un niveau de détail sans précédent. La datation au radiocarbone des glissements de terrain étudiés donne un âge d'environ 20 kyrs, ce qui suggère un rôle potentiel de l'abaissement du niveau marin pendant le dernier maximum glaciaire. Le principal facteur de préconditionnement qui affecte la stabilité des fonds marins dans le GoL est la présence de sédiments riches en argile le long des surfaces à la base des glissements, qui présentent un comportement de baisse de résistance à la déformation et agissent comme possibles plans de cisaillement. Le mécanisme exact de déclenchement responsable de la mise en place de ces grands glissements n'est pas encore clair, mais une combinaison de processus tels que l'augmentation locale et régionale de la pente due à l'halocinèse et la génération d'un excès de pression interstitielle due à l'accumulation rapide de sédiments affecte probablement la stabilité de la pente.The Gulf of Lions (GoL) is a passive margin of about 200 km length and 70 km width that extends in W-E direction from the Southern French coast to the Balearic abyssal plain (BAP) in the deep western Mediterranean. The slope of the GoL is dissected by fifteen submarine canyons, the largest one being the Petit Rhone Canyon that funnels sediment supplied by the Rhone River through the Rhone delta. Seafloor instability in the GoL occurs in canyon heads and flanks, but also in the interfluve slope areas and in the levees of the main submarine valleys. This PhD thesis aims at understanding the emplacement processes of the three largest mass transport deposits in the GoL: the Rhone Western and Eastern Mass Transport Deposits, and the BAP megaturbidite located in the abyssal plain. I present a newly available multidisciplinary dataset including geophysical, sedimentological, in-situ and laboratory geotechnical data.The study area is characterized by multiple headwall scarps. The overall morphology of the slope failures is controlled by the presence of multiple listric faults rooted in the Messinian strata. The higher resolution of newly available geophysical data, especially deep-towed seismic lines, shows the internal structure of the mass-wasting deposits in unprecedented detail. Radiocarbon dating on top of the studied mass transport deposits yields an age of about 20 kyrs, suggesting a potential role of sea-level lowering during the last glacial maximum. The main preconditioning factor that affects slope stability in the GoL is the presence of clayrich sediments within the basal surfaces of the failures that show strain-softening behaviour. The exact triggering mechanism responsible for the emplacement of these large mass transport deposits is not yet clear, but a combination of processes such as local and regional slope steepening due to halokinesis and excess pore pressure generation due to rapid sediment accumulation likely affect the slope stability