Convex Multivariable Trace Functions

For any densely defined, lower semi-continuous trace \tau on a C*-algebra A with mutually commuting C*-subalgebras A_1, A_2, ... A_n, and a convex function f of n variables, we give a short proof of the fact that the function (x_1, x_2, ..., x_n) --> \tau (f(x_1, x_2, ..., x_n)) is convex on the space \bigoplus_{i=1}^n (A_i)_{self-adjoint}. If furthermore the function f is log-convex or root-convex, so is the corresponding trace function. We also introduce a generalization of log-convexity and root-convexity called \ell-convexity, show how it applies to traces, and give a few examples. In particular we show that the trace of an operator mean is always dominated by the corresponding mean of the trace values.Comment: 13 pages, AMS TeX, Some remarks and results adde

Combined production of broilers and fruits

Combined production of broilers and fruit trees is a subject often discussed in organic fruit production in Denmark. Very little research has been carried out on this type of production system. In organic production in Denmark, nearly no pesticides are allowed, so the need for alternative pest control is large. Apple sawfly (Hoplocampa testudinea) and pear midge (Contarinia pyrivora) cause big crop losses in apples and pears respectively, in unsprayed organic fruit production. Both insects infest fruitlets and cause these to drop prematurely after which the pests pupate in the topsoil. In the present experiment a research orchard with the varieties ‘Discovery’ and ‘Conference’ were used as outdoor area for broilers to minimise the population of sawflies and pear midges, and to reduce the need for weeding and manuring. The trees were kept unsprayed. Fruit yield and fruit quality were assessed at harvest. White sticky traps were placed in the test area in order to measure the occurrence of sawfly over time. The infestation of pear midge was investigated counting the infested fruitlets in clusters on trees at the centre of the plots. The catch of apple sawflies was reduced in the combined apple and broiler production, but no significant effect on the yield or the fruit quality was seen. Experiences from on-farm research show that combining fruit and egg-production is one way to reduce the problem with apple sawfly, but poultry alone is not a sufficient way of controlling sawflies. The welfare and health of the broilers were excellent under fruit trees

Optical second harmonic generation from Wannier excitons

Excitonic effects in the linear optical response of semiconductors are well-known and the subject of countless experimental and theoretical studies. For the technologically important second order nonlinear response, however, description of excitonic effects has proved to be difficult. In this work, a simplified three-band Wannier exciton model of cubic semiconductors is applied and a closed form expression for the complex second harmonic response function including broadening is derived. Our calculated spectra are found to be in excellent agreement with the measured response near the band edge. In addition, a very substantial enhancement of the nonlinear response is predicted for the transparency region

Universal Quantum Computation in a Neutral Atom Decoherence Free Subspace

In this paper, we propose a way to achieve protected universal computation in a neutral atom quantum computer subject to collective dephasing. Our proposal relies on the existence of a Decoherence Free Subspace (DFS), resulting from symmetry properties of the errors. After briefly describing the physical system and the error model considered, we show how to encode information into the DFS and build a complete set of safe universal gates. Finally, we provide numerical simulations for the fidelity of the different gates in the presence of time-dependent phase errors and discuss their performance and practical feasibility.Comment: 7 pages, 8 figure

Error correction in ensemble registers for quantum repeaters and quantum computers

We propose to use a collective excitation blockade mechanism to identify errors that occur due to disturbances of single atoms in ensemble quantum registers where qubits are stored in the collective population of different internal atomic states. A simple error correction procedure and a simple decoherence-free encoding of ensemble qubits in the hyperfine states of alkali atoms are presented.Comment: 4 pages, 2 figure

Conditional expectations associated with quantum states

An extension of the conditional expectations (those under a given subalgebra of events and not the simple ones under a single event) from the classical to the quantum case is presented. In the classical case, the conditional expectations always exist; in the quantum case, however, they exist only if a certain weak compatibility criterion is satisfied. This compatibility criterion was introduced among others in a recent paper by the author. Then, state-independent conditional expectations and quantum Markov processes are studied. A classical Markov process is a probability measure, together with a system of random variables, satisfying the Markov property and can equivalently be described by a system of Markovian kernels (often forming a semigroup). This equivalence is partly extended to quantum probabilities. It is shown that a dynamical (semi)group can be derived from a given system of quantum observables satisfying the Markov property, and the group generators are studied. The results are presented in the framework of Jordan operator algebras, and a very general type of observables (including the usual real-valued observables or self-adjoint operators) is considered.Comment: 10 pages, the original publication is available at http://www.aip.or

Superselection in the presence of constraints

For systems which contain both superselection structure and constraints, we study compatibility between constraining and superselection. Specifically, we start with a generalisation of Doplicher-Roberts superselection theory to the case of nontrivial centre, and a set of Dirac quantum constraints and find conditions under which the superselection structures will survive constraining in some form. This involves an analysis of the restriction and factorisation of superselection structures. We develop an example for this theory, modelled on interacting QED.Comment: Latex, 38 page

Adiabatic Elimination in a Lambda System

This paper deals with different ways to extract the effective two-dimensional lower level dynamics of a lambda system excited by off-resonant laser beams. We present a commonly used procedure for elimination of the upper level, and we show that it may lead to ambiguous results. To overcome this problem and better understand the applicability conditions of this scheme, we review two rigorous methods which allow us both to derive an unambiguous effective two-level Hamiltonian of the system and to quantify the accuracy of the approximation achieved: the first one relies on the exact solution of the Schrodinger equation, while the second one resorts to the Green's function formalism and the Feshbach projection operator technique.Comment: 14 pages, 3 figure

Field efficacy of new compounds to replace copper for scab control in organic apple production

Efficacy of compounds was investigated in field experiments in Denmark and the Netherlands according to EPPO guidelines. Some Yucca extracts and potassium bicarbonate had an efficacy similar to sulphur on leaves. Addition of sulphur to Yucca 1 and to potassium bicarbonate increased the level of efficacy to that of copper. This confirms results from earlier years. Although a dose increase resulted in better efficacy, this was more prominent for Yucca1 than for potassium bicarbonate

ISO far-infrared observations of rich galaxy clusters II. Sersic 159-03

The far-infrared emission from rich galaxy clusters is investigated. Maps have been obtained by ISO at 60, 100, 135, and 200 microns using the PHT-C camera. Ground based imaging and spectroscopy were also acquired. Here we present the results for the cooling flow cluster Sersic 159-03. An infrared source coincident with the dominant cD galaxy is found. Some off-center sources are also present, but without any obvious counterparts.Comment: 6 pages, 4 postscript figures, accepted for publication in `Astronomy and Astrophysics