Deconstructing Corporate Governance: Director Primacy Without Principle?

For almost eighty years now, corporate law scholarship has centered around two elementary analytical findings made in what has once been described as the “last major work of original scholarship”within the field

The peak oil debate

For the past half-century, a debate has raged over when "peak oil" will occur—the point at which output can no longer increase and production begins to level off or gradually decline. Determining how long the oil supply will last has become even more pressing because the world’s energy supply still relies heavily on oil, and global energy demand is expected to rise steeply over the next twenty years. ; This article seeks to bring the peak oil debate into focus. The author notes that a number of factors cloud the energy outlook: Estimates of remaining resources are typically given as a range of probabilities and are thus open to interpretation. Variations also occur in estimates of future oil production and in the ways countries report their reserve data. ; The lack of a common definitional framework also confuses the debate. The author provides definitions of frequently used terms, delineating types of reserves and conventional versus nonconventional resources. She also discusses how technological innovations, government policies, and prices influence oil production. ; Regardless of the exact timing of peak oil production, the world must address the challenge of adapting to a new model of energy supply. Perhaps the world would be better served, the author notes, if the peak oil debate could be more solution-oriented, focusing on discovering the best way to transition to a world with less conventional oil rather than locking horns about discrepancies in terminology.

Coquaternionic quantum dynamics for two-level systems

The dynamical aspects of a spin- 1/2 particle in Hermitian coquaternionic quantum theory is investigated. It is shown that the time evolution exhibits three di erent characteristics, depending on the values of the parameters of the Hamiltonian. When energy eigenvalues are real, the evolution is either isomorphic to that of a complex Hermitian theory on a spherical state space, or else it remains unitary along an open orbit on a hyperbolic state space. When energy eigenvalues form a complex conjugate pair, the orbit of the time evolution closes again even though the state space is hyperbolic

Complexified coherent states and quantum evolution with non-Hermitian Hamiltonians

The complex geometry underlying the Schr\"odinger dynamics of coherent states for non-Hermitian Hamiltonians is investigated. In particular two seemingly contradictory approaches are compared: (i) a complex WKB formalism, for which the centres of coherent states naturally evolve along complex trajectories, which leads to a class of complexified coherent states; (ii) the investigation of the dynamical equations for the real expectation values of position and momentum, for which an Ehrenfest theorem has been derived in a previous paper, yielding real but non-Hamiltonian classical dynamics on phase space for the real centres of coherent states. Both approaches become exact for quadratic Hamiltonians. The apparent contradiction is resolved building on an observation by Huber, Heller and Littlejohn, that complexified coherent states are equivalent if their centres lie on a specific complex Lagrangian manifold. A rich underlying complex symplectic geometry is unravelled. In particular a natural complex structure is identified that defines a projection from complex to real phase space, mapping complexified coherent states to their real equivalents.Comment: 18 pages, small improvements made, similar to published versio

Classical-quantum correspondence in bosonic two-mode conversion systems: polynomial algebras and Kummer shapes

Bosonic quantum conversion systems can be modeled by many-particle single-mode Hamiltonians describing a conversion of $n$ molecules of type A into $m$ molecules of type B and vice versa. These Hamiltonians are analyzed in terms of generators of a polynomially deformed $su(2)$ algebra. In the mean-field limit of large particle numbers, these systems become classical and their Hamiltonian dynamics can again be described by polynomial deformations of a Lie algebra, where quantum commutators are replaced by Poisson brackets. The Casimir operator restricts the motion to Kummer shapes, deformed Bloch spheres with cusp singularities depending on $m$ and $n$. It is demonstrated that the many-particle eigenvalues can be recovered from the mean-field dynamics using a WKB type quantization condition. The many-particle state densities can be semiclassically approximated by the time-periods of periodic orbits, which show characteristic steps and singularities related to the fixed points, whose bifurcation properties are analyzed.Comment: 13 pages, 13 figure