The Canonical Form of the Rabi Hamiltonian

The Rabi Hamiltonian, describing the coupling of a two-level system to a single quantized boson mode, is studied in the Bargmann-Fock representation. The corresponding system of differential equations is transformed into a canonical form in which all regular singularities between zero and infinity have been removed. The canonical or Birkhoff-transformed equations give rise to a two-dimensional eigenvalue problem, involving the energy and a transformational parameter which affects the coupling strength. The known isolated exact solutions of the Rabi Hamiltonian are found to correspond to the uncoupled form of the canonical system.Comment: 17 pages, LaTeX, no figures, to appear in J.Math.Phy

The 'Chemical Mechanics' of the Periodic Table

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Rock and roll bands, (in)complete contracts and creativity

Members of a rock and roll band are endowed with different creativity. They match and eventually obtain credit for song writing as well as a share of the returns from sales. More creative members increase the probability of success but may also claim a larger share of the pie. In our theoretical model, the nature of matching (postive or negative assortative) as well as the covariation between the probability of having a “hit” and the dispersion of credits given to individual members are a function of the completeness of contracting. When members adopt a “gentleman’s agreement” to share credits equally, the covariation between the probability of a hit and the dispersion of credits is negative, which is the consequence of positive assortative matching in creativity. The data show that the relation between dispersion and success is significantly negative, and that rock bands are thus likely to sign incomplete contracts.overlapping generations, resource management, common pool resource, spatial interdependence, strategic behaviour, cooperative behaviour

Ecophisiological aspects in horticultural research

Peer Reviewe

CAD enabled trajectory optimization and accurate motion control for repetitive tasks

As machine users generally only define the start and end point of the movement, a large trajectory optimization potential rises for single axis mechanisms performing repetitive tasks. However, a descriptive mathematical model of the mecha- nism needs to be defined in order to apply existing optimization techniques. This is usually done with complex methods like virtual work or Lagrange equations. In this paper, a generic technique is presented to optimize the design of point-to-point trajectories by extracting position dependent properties with CAD motion simulations. The optimization problem is solved by a genetic algorithm. Nevertheless, the potential savings will only be achieved if the machine is capable of accurately following the optimized trajectory. Therefore, a feedforward motion controller is derived from the generic model allowing to use the controller for various settings and position profiles. Moreover, the theoretical savings are compared with experimental data from a physical set-up. The results quantitatively show that the savings potential is effectively achieved thanks to advanced torque feedforward with a reduction of the maximum torque by 12.6% compared with a standard 1/3-profil

Chemical Bonding in the Boron Buckyball

A symmetry analysis of the valence shell in the boron buckyball B80, shows a perfect match with the symmetry of the valence shell in C60 .The cap atoms participate in the bonding by 30 orbitals which transform as the sigma bonds along the 6-6 edges. Far reaching consequences for chemical and physical properties of B80, which until now only exists in silico, are expected.Comment: 2 pages, 1 Figur