The Lorentzian distance formula in noncommutative geometry

For almost twenty years, a search for a Lorentzian version of the well-known Connes' distance formula has been undertaken. Several authors have contributed to this search, providing important milestones, and the time has now come to put those elements together in order to get a valid and functional formula. This paper presents a historical review of the construction and the proof of a Lorentzian distance formula suitable for noncommutative geometry.Comment: 16 pages, final form, few references adde

A quantum theoretical explanation for probability judgment errors

A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction, disjunction, inverse, and conditional fallacies, as well as unpacking effects and partitioning effects. Quantum probability theory is a general and coherent theory based on a set of (von Neumann) axioms which relax some of the constraints underlying classic (Kolmogorov) probability theory. The quantum model is compared and contrasted with other competing explanations for these judgment errors including the representativeness heuristic, the averaging model, and a memory retrieval model for probability judgments. The quantum model also provides ways to extend Bayesian, fuzzy set, and fuzzy trace theories. We conclude that quantum information processing principles provide a viable and promising new way to understand human judgment and reasoning

Tailoring the ground state of the ferrimagnet La2Ni(Ni1/3Sb2/3)O6

We report on the magnetic and structural properties of La2Ni(Ni1/3Sb2/3)O6 in polycrystal, single crystal and thin film samples. We found that this material is a ferrimagnet (Tc ~ 100 K) which possesses a very distinctive and uncommon feature in its virgin curve of the hysteresis loops. We observe that bellow 20 K it lies outside the hysteresis cycle, and this feature was found to be an indication of a microscopically irreversible process possibly involving the interplay of competing antiferromagnetic interactions that hinder the initial movement of domain walls. This initial magnetic state is overcome by applying a temperature dependent characteristic field. Above this field, an isothermal magnetic demagnetization of the samples yield a ground state different from the initial thermally demagnetized one.Comment: 21 pages, 8 figures, submitted to JMM

T-Dualities and Doubled Geometry of the Principal Chiral Model

The Principal Chiral Model (PCM) defined on the group manifold of SU(2) is here investigated with the aim of getting a further deepening of its relation with Generalized and Doubled Geometry. A one-parameter family of equivalent Hamiltonian descriptions is introduced, and cast into the form of Born geometries. Then O(3,3) duality transformations of the target phase space are performed and we show that the resulting dual models are defined on the group SB(2,C) which is the Poisson-Lie dual of SU(2) in the Iwasawa decomposition of the Drinfel'd double SL(2, C). Moreover, starting from the Lagrangian approach, a new kind of duality is found between the SU(2) PCM and the natural one defined on SB(2,C) which is not an isometry of the target phase space. A parent action with doubled degrees of freedom and configuration space SL(2, C) is then defined that reduces to either one of the dually related models, once suitable constraints are implemented.Comment: 41 pages, revised version published in JHE

Atomic spin sensitive dissipation on magnetic surfaces

We identify the mechanism of energy dissipation relevant to spin-sensitive nanomechanics including the recently introduced magnetic exchange force microscopy, where oscillating magnetic tips approach surface atomic spins. The tip-surface exchange couples spin and atom coordinates, leading to a spin-phonon problem with Caldeira-Leggett type dissipation. In the overdamped regime, that can lead to a hysteretic flip of the local spin with a large spin-dependent dissipation, even down to the very low experimental tip oscillation frequencies, describing recent observations for Fe tips on NiO. A phase transition to an underdamped regime with dramatic drop of magnetic tip dissipation should in principle be possible by tuning tip-surface distance.Comment: 4 pages, 4 figure

Cooling a magnetic resonance force microscope via the dynamical back-action of nuclear spins

We analyze the back-action influence of nuclear spins on the motion of the cantilever of a magnetic force resonance microscope. We calculate the contribution of nuclear spins to the damping and frequency shift of the cantilever. We show that, at the Rabi frequency, the energy exchange between the cantilever and the spin system cools or heats the cantilever depending on the sign of the high-frequency detuning. We also show that the spin noise leads to a significant damping of the cantilever motion.Comment: 15 pqges, 11 figures. The last part of Section IV.A and Section IV B were rewritten. We added three new graphs: Figs. 5, 7, 9 and all graphs in this subsection were recalculated for T=600 mK as in the experiment. Several new references were adde

Magnetic properties of the double perovskites LaPbMSbO6 (M = Mn, Co and Ni)

New double perovskites LaPbMSbO6, where M2+ = Mn2+, Co2+, and Ni2+, were synthesized as polycrystals by an aqueous synthetic route at temperatures below 1000 oC. All samples are monoclinic, space group P21/n, as obtained from Rietveld analysis of X-ray powder diffraction patterns. The distribution of M2+ and Sb5+ among the two octahedral sites have 3% of disorder for M2+ = Ni2+, whereas for M2+ = Mn2+ and Co2+ less disorder is found. The three samples have an antiferromagnetic transition, due to the antiferromagnetic coupling between M2+ through super-superexchange paths M2+ - O2- - Sb5+ - O2- - M2+. Transition temperatures are low: 8, 10 and 17 K for Mn2+, Co2+, and Ni2+ respectively, as a consequence of the relatively long distances between the magnetic ions M2+. Besides, for LaPbMnSbO6 a small transition at 45 K was found, with ferrimagnetic characteristics, possibly as a consequence of a small disorder between Mn2+ and Sb5+. This disorder would give additional and shorter interaction paths: superexchange Mn2+ - O2- - Mn2+.Comment: 4 pages, 4 figures included. Manuscript submitted to IEEE Transactions on Magnetics, proceedings of the LAW3M 2013 conferenc