Contractions of low-dimensional nilpotent Jordan algebras

In this paper we classify the laws of three-dimensional and four-dimensional nilpotent Jordan algebras over the field of complex numbers. We describe the irreducible components of their algebraic varieties and extend contractions and deformations among them. In particular, we prove that J2 and J3 are irreducible and that J4 is the union of the Zariski closures of two rigid Jordan algebras.Comment: 12 pages, 3 figure

Violation of a Bell inequality in particle physics experimentally verified?

Relevant aspects for testing Bell inequalities with entangled meson-antimeson systems are analyzed. In particular, we argue that the result of A. Go, J. Mod. Optics 51, 991 (2004), which nicely illustrate the quantum entanglement of B-meson pairs, cannot be considered as a Bell-test refuting local realism.Comment: 9 page

Shallow structure beneath the Central Volcanic Complex of Tenerife from new gravity data: implications for its evolution and recent reactivation

We present a new local Bouguer anomaly map of the Central Volcanic Complex (CVC) of Tenerife, Spain, constructed from the amalgamation of 323 new high precision gravity measurements with existing gravity data from 361 observations. The new anomaly map images the high-density core of the CVC and the pronounced gravity low centred in the Las Cañadas caldera in greater detail than previously available. Mathematical construction of a sub-surface model from the local anomaly data, employing a 3D inversion based on 'growing' the sub-surface density distribution via the aggregation of cells, enables mapping of the shallow structure beneath the complex, giving unprecedented insights into the sub-surface architecture. We find the resultant density distribution in agreement with geological and other geophysical data. The modelled sub-surface structure supports a vertical collapse origin of the caldera, and maps the headwall of the ca. 180 ka Icod landslide, which appears to lie buried beneath the Pico Viejo–Pico Teide stratovolcanic complex. The results allow us to put into context the recorded ground deformation and gravity changes at the CVC during its reactivation in spring 2004 in relation to its dominant structural building blocks. For example, the areas undergoing the most significant changes at depth in recent years are underlain by low-density material and are aligned along long-standing structural entities, which have shaped this volcanic ocean island over the past few million years

On the structure of maximal solvable extensions and of Levi extensions of nilpotent algebras

We establish an improved upper estimate on dimension of any solvable algebra s with its nilradical isomorphic to a given nilpotent Lie algebra n. Next we consider Levi decomposable algebras with a given nilradical n and investigate restrictions on possible Levi factors originating from the structure of characteristic ideals of n. We present a new perspective on Turkowski's classification of Levi decomposable algebras up to dimension 9.Comment: 21 pages; major revision - one section added, another erased; author's version of the published pape

An open quantum system approach to EPR correlations in K0-K0 system

We find the time evolution of the system of two non-interacting unstable particles, distinguishable as well as identical ones, in arbitrary reference frame having only the Kraus operators governing the evolution of its components in the rest frame. We than calculate in the rigorous way Einstein-Podolsky-Rosen quantum correlation functions for K0-K0 system in the singlet state taking into account CP-violation and decoherence and show that the results are exactly the same despite the fact we treat kaons as distinguishable or identical particles which means that the statistics of the particles plays no role, at least in considered cases.Comment: 14 pp. no fig

Invariants of solvable rigid Lie algebras up to dimension 8

The invariants of all complex solvable rigid Lie algebras up to dimension eight are computed. Moreover we show, for rank one solvable algebras, some criteria to deduce to non-existence of non-trivial invariants or the existence of fundamental sets of invariants formed by rational functions of the Casimir invariants of the associated nilradical.Comment: 16 pages, 7 table

All solvable extensions of a class of nilpotent Lie algebras of dimension n and degree of nilpotency n-1

We construct all solvable Lie algebras with a specific n-dimensional nilradical n_(n,2) (of degree of nilpotency (n-1) and with an (n-2)-dimensional maximal Abelian ideal). We find that for given n such a solvable algebra is unique up to isomorphisms. Using the method of moving frames we construct a basis for the Casimir invariants of the nilradical n_(n,2). We also construct a basis for the generalized Casimir invariants of its solvable extension s_(n+1) consisting entirely of rational functions of the chosen invariants of the nilradical.Comment: 19 pages; added references, changes mainly in introduction and conclusions, typos corrected; submitted to J. Phys. A, version to be publishe

Bell-inequalities for K0K0ˉK^0 \bar{K^0} Pairs from Φ\Phi-Resonance Decays

We analyze the premises of recent propositions to test local realism via Bell-inequalities using neutral kaons from $\Phi$-resonance decays as entangled EPR-pairs. We pay special attention to the derivation of Bell-inequalities, or related expressions, for unstable and oscillating kaon `quasi-spin' states and to the possibility of the actual identification of these states through their associated decay modes. We discuss an indirect method to extract probabilities to find these states by combining experimental information with theoretical input. However, we still find inconsistencies in previous derivations of Bell-inequalities. We show that the identification of the quasi-spin states via their associated decay mode does not allow the free choice to perform different tests on them, a property which is crucial to establish the validity of any Bell-inequality in the context of local realism. In view of this we propose a different kind of Bell-inequality in which the free choice or adjustability of the experimental set-up is guaranteed. We also show that the proposed inequalities are violated by quantum mechanics.Comment: 22 pages. Late

Space-Dependent Probabilities for K0−K0ˉK^0-\bar{K^0} Oscillations

We analyze $K^0-\bar{K^0}$ oscillations in space in terms of propagating wave packets with coherent $K_S$ and $K_L$ components. The oscillation probabilities $P_{K^0 \to K^0} (x)$ and $P_{K^0 \to \bar{K^0}} (x)$ depending only on the distance $x$, are defined through the time integration of a current density $j(x,t)$ . The definition is such that it coincides with the experimental setting, thus avoiding some ambiguities and clarifying some controversies that have been discussed recently.Comment: 11 pages, late

Three-party entanglement from positronium

The decay of ortho-positronium into three photons produces a physical realization of a pure state with three-party entanglement. Its quantum correlations are analyzed using recent results on quantum information theory, looking for the final state which has the maximal amount of GHZ-like correlations. This state allows for a statistical dismissal of local realism stronger than the one obtained using any entangled state of two spin one-half particles.Comment: REVTEX, 13 pages, 3 figure