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

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

Signatures of three coalescing eigenfunctions

Parameter dependent non-Hermitian quantum systems typically not only possess eigenvalue degeneracies, but also degeneracies of the corresponding eigenfunctions at exceptional points. While the effect of two coalescing eigenfunctions on cyclic parameter variation is well investigated, little attention has hitherto been paid to the effect of more than two coalescing eigenfunctions. Here a characterisation of behaviours of symmetric Hamiltonians with three coalescing eigenfunctions is presented, using perturbation theory for non-Hermitian operators. Two main types of parameter perturbations need to be distinguished, which lead to characteristic eigenvalue and eigenvector patterns under cyclic variation. A physical system is introduced for which both behaviours might be experimentally accessible.Comment: 14 pages, 4 figures. Typos corrected, slightly extended, to appear in J. Phys.

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

Propagation of Gaussian beams in the presence of gain and loss

We consider the propagation of Gaussian beams in a waveguide with gain and loss in the paraxial approximation governed by the Schr\"odinger equation. We derive equations of motion for the beam in the semiclassical limit that are valid when the waveguide profile is locally well approximated by quadratic functions. For Hermitian systems, without any loss or gain, these dynamics are given by Hamilton's equations for the center of the beam and its conjugate momentum. Adding gain and/or loss to the waveguide introduces a non-Hermitian component, causing the width of the Gaussian beam to play an important role in its propagation. Here we show how the width affects the motion of the beam and how this may be used to filter Gaussian beams located at the same initial position based on their width

Instant restore after a media failure

Media failures usually leave database systems unavailable for several hours until recovery is complete, especially in applications with large devices and high transaction volume. Previous work introduced a technique called single-pass restore, which increases restore bandwidth and thus substantially decreases time to repair. Instant restore goes further as it permits read/write access to any data on a device undergoing restore--even data not yet restored--by restoring individual data segments on demand. Thus, the restore process is guided primarily by the needs of applications, and the observed mean time to repair is effectively reduced from several hours to a few seconds. This paper presents an implementation and evaluation of instant restore. The technique is incrementally implemented on a system starting with the traditional ARIES design for logging and recovery. Experiments show that the transaction latency perceived after a media failure can be cut down to less than a second and that the overhead imposed by the technique on normal processing is minimal. The net effect is that a few "nines" of availability are added to the system using simple and low-overhead software techniques

Mixed-state evolution in the presence of gain and loss

A model is proposed that describes the evolution of a mixed state of a quantum system for which gain and loss of energy or amplitude are present. Properties of the model are worked out in detail. In particular, invariant subspaces of the space of density matrices corresponding to the fixed points of the dynamics are identified, and the existence of a transition between the phase in which gain and loss are balanced and the phase in which this balance is lost is illustrated in terms of the time average of observables. The model is extended to include a noise term that results from a uniform random perturbation generated by white noise. Numerical studies of example systems show the emergence of equilibrium states that suppress the phase transition.Comment: 5 pages, 2 figures (published version