Dualities between Poisson brackets and antibrackets

Recently it has been shown that antibrackets may be expressed in terms of Poisson brackets and vice versa for commuting functions in the original bracket. Here we also introduce generalized brackets involving higher antibrackets or higher Poisson brackets where the latter are of a new type. We give generating functions for these brackets for functions in arbitrary involutions in the original bracket. We also give master equations for generalized Maurer-Cartan equations. The presentation is completely symmetric with respect to Poisson brackets and antibrackets.Comment: 24 pages,Latexfile,corrected (2.7-8) and removed text between (2.9) and (2.10

Real-time detection of single electron tunneling using a quantum point contact

We observe individual tunnel events of a single electron between a quantum dot and a reservoir, using a nearby quantum point contact (QPC) as a charge meter. The QPC is capacitively coupled to the dot, and the QPC conductance changes by about 1% if the number of electrons on the dot changes by one. The QPC is voltage biased and the current is monitored with an IV-convertor at room temperature. We can resolve tunnel events separated by only 8 $\mu$s, limited by noise from the IV-convertor. Shot noise in the QPC sets a 25 ns lower bound on the accessible timescales.Comment: 3 pages, 3 figures, submitte

Soil biological quality of grassland fertilized with adjusted cattle manure slurries in comparison with organic and inorganic fertilizers

We studied the effect of five fertilizers (including two adjusted manure slurries) and an untreated control on soil biota and explored the effect on the ecosystem services they provided. Our results suggest that the available N (NO3- and NH4+) in the soil plays a central role in the effect of fertilizers on nematodes and microorganisms. Microorganisms are affected directly through nutrient availability and indirectly through grass root mass. Nematodes are affected indirectly through microbial biomass and grass root mass. A lower amount of available N in the treatment with inorganic fertilizer was linked to a higher root mass and a higher abundance and proportion of herbivorous nematodes. A higher amount of available N in the organic fertilizer treatments resulted in a twofold higher bacterial activity (measured as bacterial growth rate, viz. thymidine incorporation), a higher proportion of bacterivorous nematodes, a 30% higher potential N mineralization (aerobic incubation), and 25–50% more potentially mineralizable N (anaerobic incubation). Compared to inorganic fertilizer, organic fertilization increased the C total, the N total, the activity of decomposers, and the supply of nutrients via the soil food web. Within the group of organic fertilizers, there was no significant difference in C total, abundances of soil biota, and the potential N mineralization rate. There were no indications that farmyard manure or the adjusted manure slurries provided the ecosystem service “supply of nutrients” better than normal manure slurry. Normal manure slurry provided the highest bacterial activity and the highest amount of mineralizable N and it was the only fertilizer resulting in a positive trend in grass yield over the years 2000–2005. The number of earthworm burrows was higher in the treatments with organic fertilizers compared to the one with the inorganic fertilizer, which suggests that organic fertilizers stimulate the ecosystem service of water regulation more than inorganic fertilizer. The trend towards higher epigeic earthworm numbers with application of farmyard manure and one of the adjusted manure slurries, combined with the negative relation between epigeic earthworms and bulk density and a significantly lower penetration resistance in the same fertilizer types, is preliminary evidence that these two organic fertilizer types contribute more to the service of soil structure maintenance than inorganic fertilize

Reversing quantum trajectories with analog feedback

We demonstrate the active suppression of transmon qubit dephasing induced by dispersive measurement, using parametric amplification and analog feedback. By real-time processing of the homodyne record, the feedback controller reverts the stochastic quantum phase kick imparted by the measurement on the qubit. The feedback operation matches a model of quantum trajectories with measurement efficiency $\tilde{\eta} \approx 0.5$, consistent with the result obtained by postselection. We overcome the bandwidth limitations of the amplification chain by numerically optimizing the signal processing in the feedback loop and provide a theoretical model explaining the optimization result.Comment: 5 pages, 4 figures, and Supplementary Information (7 figures

The Einstein 3-form G_a and its equivalent 1-form L_a in Riemann-Cartan space

The definition of the Einstein 3-form G_a is motivated by means of the contracted 2nd Bianchi identity. This definition involves at first the complete curvature 2-form. The 1-form L_a is defined via G_a = L^b \wedge #(o_b \wedge o_a). Here # denotes the Hodge-star, o_a the coframe, and \wedge the exterior product. The L_a is equivalent to the Einstein 3-form and represents a certain contraction of the curvature 2-form. A variational formula of Salgado on quadratic invariants of the L_a 1-form is discussed, generalized, and put into proper perspective.Comment: LaTeX, 13 Pages. To appear in Gen. Rel. Gra

The Chrono-geometrical Structure of Special and General Relativity: a Re-Visitation of Canonical Geometrodynamics

A modern re-visitation of the consequences of the lack of an intrinsic notion of instantaneous 3-space in relativistic theories leads to a reformulation of their kinematical basis emphasizing the role of non-inertial frames centered on an arbitrary accelerated observer. In special relativity the exigence of predictability implies the adoption of the 3+1 point of view, which leads to a well posed initial value problem for field equations in a framework where the change of the convention of synchronization of distant clocks is realized by means of a gauge transformation. This point of view is also at the heart of the canonical approach to metric and tetrad gravity in globally hyperbolic asymptotically flat space-times, where the use of Shanmugadhasan canonical transformations allows the separation of the physical degrees of freedom of the gravitational field (the tidal effects) from the arbitrary gauge variables. Since a global vision of the equivalence principle implies that only global non-inertial frames can exist in general relativity, the gauge variables are naturally interpreted as generalized relativistic inertial effects, which have to be fixed to get a deterministic evolution in a given non-inertial frame. As a consequence, in each Einstein's space-time in this class the whole chrono-geometrical structure, including also the clock synchronization convention, is dynamically determined and a new approach to the Hole Argument leads to the conclusion that "gravitational field" and "space-time" are two faces of the same entity. This view allows to get a classical scenario for the unification of the four interactions in a scheme suited to the description of the solar system or our galaxy with a deperametrization to special relativity and the subsequent possibility to take the non-relativistic limit.Comment: 33 pages, Lectures given at the 42nd Karpacz Winter School of Theoretical Physics, "Current Mathematical Topics in Gravitation and Cosmology", Ladek, Poland, 6-11 February 200

Deterministic delivery of remote entanglement on a quantum network

Large-scale quantum networks promise to enable secure communication, distributed quantum computing, enhanced sensing and fundamental tests of quantum mechanics through the distribution of entanglement across nodes. Moving beyond current two-node networks requires the rate of entanglement generation between nodes to exceed their decoherence rates. Beyond this critical threshold, intrinsically probabilistic entangling protocols can be subsumed into a powerful building block that deterministically provides remote entangled links at pre-specified times. Here we surpass this threshold using diamond spin qubit nodes separated by 2 metres. We realise a fully heralded single-photon entanglement protocol that achieves entangling rates up to 39 Hz, three orders of magnitude higher than previously demonstrated two-photon protocols on this platform. At the same time, we suppress the decoherence rate of remote entangled states to 5 Hz by dynamical decoupling. By combining these results with efficient charge-state control and mitigation of spectral diffusion, we are able to deterministically deliver a fresh remote state with average entanglement fidelity exceeding 0.5 at every clock cycle of $\sim$100 ms without any pre- or post-selection. These results demonstrate a key building block for extended quantum networks and open the door to entanglement distribution across multiple remote nodes.Comment: v2 - updated to include relevant citatio

A local characterisation for static charged black holes

We obtain a purely local characterisation that singles out the Majumdar-Papapetrou class, the near-horizon Bertotti-Robinson geometry and the Reissner-Nordstr\"om exterior solution, together with its plane and hyperbolic counterparts, among the static electrovacuum spacetimes. These five classes are found to form the whole set of static Einstein-Maxwell fields without sources and conformally flat space of orbits, this is, the conformastat electrovacuum spacetimes. The main part of the proof consists in showing that a functional relationship between the gravitational and electromagnetic potentials must always exist. The classification procedure provides also an improved characterisation of Majumdar-Papapetrou, by only requiring a conformally flat space of orbits with a vanishing Ricci scalar of the usual conveniently rescaled 3-metric. A simple global consideration allows us to state that the asymptotically flat subset of the Majumdar-Papapetrou class and the Reissner-Nordstr\"om exterior solution are the only asymptotically flat conformastat electrovacuum spacetimes.Comment: LaTeX; 31 pages. Uses iopart style file