A discussion on particle number and quantum indistinguishability

The concept of individuality in quantum mechanics shows radical differences from the concept of individuality in classical physics, as E. Schroedinger pointed out in the early steps of the theory. Regarding this fact, some authors suggested that quantum mechanics does not possess its own language, and therefore, quantum indistinguishability is not incorporated in the theory from the beginning. Nevertheless, it is possible to represent the idea of quantum indistinguishability with a first order language using quasiset theory (Q). In this work, we show that Q cannot capture one of the most important features of quantum non individuality, which is the fact that there are quantum systems for which particle number is not well defined. An axiomatic variant of Q, in which quasicardinal is not a primitive concept (for a kind of quasisets called finite quasisets), is also given. This result encourages the searching of theories in which the quasicardinal, being a secondary concept, stands undefined for some quasisets, besides showing explicitly that in a set theory about collections of truly indistinguishable entities, the quasicardinal needs not necessarily be a primitive concept.Comment: 46 pages, no figures. Accepted by Foundations of Physic

On the lattice structure of probability spaces in quantum mechanics

Let C be the set of all possible quantum states. We study the convex subsets of C with attention focused on the lattice theoretical structure of these convex subsets and, as a result, find a framework capable of unifying several aspects of quantum mechanics, including entanglement and Jaynes' Max-Ent principle. We also encounter links with entanglement witnesses, which leads to a new separability criteria expressed in lattice language. We also provide an extension of a separability criteria based on convex polytopes to the infinite dimensional case and show that it reveals interesting facets concerning the geometrical structure of the convex subsets. It is seen that the above mentioned framework is also capable of generalization to any statistical theory via the so-called convex operational models' approach. In particular, we show how to extend the geometrical structure underlying entanglement to any statistical model, an extension which may be useful for studying correlations in different generalizations of quantum mechanics.Comment: arXiv admin note: substantial text overlap with arXiv:1008.416

A quantum logical and geometrical approach to the study of improper mixtures

We study improper mixtures from a quantum logical and geometrical point of view. Taking into account the fact that improper mixtures do not admit an ignorance interpretation and must be considered as states in their own right, we do not follow the standard approach which considers improper mixtures as measures over the algebra of projections. Instead of it, we use the convex set of states in order to construct a new lattice whose atoms are all physical states: pure states and improper mixtures. This is done in order to overcome one of the problems which appear in the standard quantum logical formalism, namely, that for a subsystem of a larger system in an entangled state, the conjunction of all actual properties of the subsystem does not yield its actual state. In fact, its state is an improper mixture and cannot be represented in the von Neumann lattice as a minimal property which determines all other properties as is the case for pure states or classical systems. The new lattice also contains all propositions of the von Neumann lattice. We argue that this extension expresses in an algebraic form the fact that -alike the classical case- quantum interactions produce non trivial correlations between the systems. Finally, we study the maps which can be defined between the extended lattice of a compound system and the lattices of its subsystems.Comment: submitted to the Journal of Mathematical Physic

Simplified model of interconnect layers under a spiral inductor

We demonstrate the feasibility of using effective medium theory to reduce the computational complexity of full-wave models of inductors that are placed over interconnects. Placing inductors over interconnects is one way that designers can tackle the problem of reducing overall chip size, however this has heretofore been a difficult option to evaluate because of the prohibitive memory requirements and run times for detailed simulations of the inductor. Here we replace the interconnects with a homogeneous equivalent layer that mimics their impact on the inductor to within 2% error, but reducing runtime and memory use by 90% or more

Second-Generation Coil Design of the Nb3Sn low-β Quadrupole for the High Luminosity LHC

As part of the Large Hadron Collider (LHC) Luminosity upgrade program, the U.S.-LHC Accelerator Research Program collaboration and CERN are working together to design and build a 150-mm aperture Nb3Sn quadrupole for the LHC interaction regions. A first series of 1.5-m-long coils was fabricated and assembled in a first short model. A detailed visual inspection of the coils was carried out to investigate cable dimensional changes during heat treatment and the position of the windings in the coil straight section and in the end region. The analyses allow identifying a set of design changes which, combined with a fine tune of the cable geometry and a field quality optimization, were implemented in a new second-generation coil design. In this paper, we review the main characteristics of the first generation coils, describe the modification in coil layout and discuss their impact on parts design and magnet analysis

No labeling quantum mechanics of indiscernible particles

Our aim in this paper is to show an example of the formalism we have developed to avoid the label-tensor-product-vector-space-formalism of quantum mechanics when dealing with indistinguishable quanta. States in this new vector space, that we call the Q-space, refer only to occupation numbers and permutation operators act as the identity operator on them, reflecting in the formalism the unobservability of permutations, a goal of quasi-set theory.Instituto de Física La Plat

Progress on HL-LHC Nb3Sn Magnets

The high-luminosity Large Hadron Collider (HL-LHC) project aims at allowing to increase the collisions in the LHC by a factor of ten in the decade 2025-2035. One essential element is the superconducting magnet around the interaction region points, where the large aperture magnets will be installed to allow to further reduce the beam size in the interaction point. The core of this upgrade is the Nb Sn triplet, made up of 150-mm aperture quadrupoles in the range of 7-8 m. The project is being shared between the European Organization for Nuclear Research and the US Accelerator Upgrade Program, based on the same design, and on the two strand technologies. The project is ending the short model phase, and entering the prototype construction. We will report on the main results of the short model program, including the quench performance and field quality. A second important element is the 11 T dipole that replaces a standard dipole making space for additional collimators. The magnet is also ending the model development and entering the prototype phase. A critical point in the design of this magnet is the large current density, allowing increase of the field from 8 to 11 T with the same coil cross section as in the LHC dipoles. This is also the first two-in-one Nb Sn magnet developed so far. We will report the main results on the test and the critical aspects. 3

No labeling quantum mechanics of indiscernible particles

Our aim in this paper is to show an example of the formalism we have developed to avoid the label-tensor-product-vector-space-formalism of quantum mechanics when dealing with indistinguishable quanta. States in this new vector space, that we call the Q-space, refer only to occupation numbers and permutation operators act as the identity operator on them, reflecting in the formalism the unobservability of permutations, a goal of quasi-set theory.Comment: submitted to the special issue of the International Journal of Theoretical Physics dedicated to the IQSA Meeting "Quantum Structures Brussels-Gdansk '08

Origin and geochemical evolution of the Madeira-Tore Rise (eastern North Atlantic)

The Madeira-Tore Rise, located ∼700 km off the NW African coast, forms a prominent ridge in the east Atlantic. The age and origin of the rise are controversial. This study presents major and trace element, Sr, Nd, Pb, Hf isotope and 40Ar/39Ar age determinations from volcanic rocks dredged from different sites along the rise. In addition, isotopic compositions of rock samples from Great Meteor Seamount in the central Atlantic are presented. The new radiometric and paleontologically constrained ages identify two major episodes of volcanism: The first is the base of the rise (circa 80 to >95 Ma) and the second is seamounts on the rise (0.5–16 Ma). It is proposed that interaction of the Canary hot spot with the Mid-Atlantic spreading center formed the deep basement of the Madeira-Tore Rise and the J-Anomaly Ridge west of the Atlantic spreading center in the Mid-Cretaceous. Age and geochemical data and plate tectonic reconstructions suggest, however, that the recovered Late Cretaceous volcanic rocks represent late stage volcanism from the time when the Madeira-Tore Rise was still close to the Canary hot spot. Long after moving away from the influence of the Canary hot spot, the Madeira-Tore Rise was overprinted by late Cenozoic volcanism. Miocene to Pleistocene volcanism at the northern end of the rise can be best explained by decompression mantle melting beneath extensional sectors of the Azores-Gibraltar Fracture Zone (African-Eurasian plate boundary). The geochemical compositions of these volcanic rocks suggest that the magmas were variably contaminated by enriched material within or derived by melting of enriched material underplated at the base of the lithosphere, possibly originating from the Cretaceous Canary plume. Alternatively, these late Cenozoic volcanic rocks may have derived from decompression melting of enriched pyroxenitic/eclogitic material in the upper mantle. Isotopically more depleted Pliocene to Pleistocene volcanism at the southern end of the Madeira-Tore Rise may be related to the nearby Madeira hot spot