Faster than Hermitian Time Evolution

For any pair of quantum states, an initial state |I> and a final quantum state |F>, in a Hilbert space, there are many Hamiltonians H under which |I> evolves into |F>. Let us impose the constraint that the difference between the largest and smallest eigenvalues of H, E_max and E_min, is held fixed. We can then determine the Hamiltonian H that satisfies this constraint and achieves the transformation from the initial state to the final state in the least possible time \tau. For Hermitian Hamiltonians, \tau has a nonzero lower bound. However, among non-Hermitian PT-symmetric Hamiltonians satisfying the same energy constraint, \tau can be made arbitrarily small without violating the time-energy uncertainty principle. The minimum value of \tau can be made arbitrarily small because for PT-symmetric Hamiltonians the path from the vector |I> to the vector |F>, as measured using the Hilbert-space metric appropriate for this theory, can be made arbitrarily short. The mechanism described here is similar to that in general relativity in which the distance between two space-time points can be made small if they are connected by a wormhole. This result may have applications in quantum computing.Comment: This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Worship in small churches

The article advocates and elaborates a theological point of view with respect to worship that is in the interest of the small church and that the small church is in a unique position to advocate. Specific rubrical proposals are made. \u27The means of grace, i.e., the Word and Sacraments, are the central and only indispensable elements in worship. The smaller amount of human resources available to small churches can lead them to focus on these means of grace. This focus is an outstanding strength\u27

An efficiency wage - imperfect information model of the aggregate supply curve

This study derives a reduced-form equation for the aggregate supply curve from a model in which firms pay efficiency wages and workers have imperfect information about average wages at other firms. If specific assumptions are made about workers’ expectations of average wages and about aggregate demand, the model predicts how the aggregate demand and supply curves shift and how output and prices adjust in response to demand shocks and supply shocks. The model also provides an alternative explanation for Lucas’ (1973) finding that the AS curve is steeper in countries with greater inflation variability.Aggregate supply curve; efficiency wages; imperfect information

Optimization of slender wings for center-of-pressure shift due to change in Mach number

It is observed that the center of pressure on a wing shifts as the Mach number is changed. Such shifts are in general undesirable and are sometimes compensated for by actively shifting the center of gravity of the aircraft or by using active stability controls. To avoid this complication, it is desirable to design the wings of a high speed aircraft so as to minimize the extent of the center-of-pressure shifts. This, together with a desire to minimize the center-of-pressure shifts in missile control surfaces, provides the motivation for this project. There are many design parameters which affect center-of-pressure shifts, but it is expected that the largest effects are due to the wing planform. Thus, for the sake of simplicity, this study is confined to an investigation of thin, flat, (i.e., no camber or twist), relatively slender, pointed wings flying at a small angle of attack. Once the dependence of the center of pressure on planform and Mach number is understood, we can expect to investigate the sensitivity of the center-of-pressure shifts to various other parameters

The force of gravity in Schwarzschild and Gullstrand-Painlev\'e coordinates

We derive the exact equations of motion (in Newtonian, F=ma, form) for test masses in Schwarzschild and Gullstrand-Painlev\'e coordinates. These equations of motion are simpler than the usual geodesic equations obtained from Christoffel tensors in that the affine parameter is eliminated. The various terms can be compared against tests of gravity. In force form, gravity can be interpreted as resulting from a flux of superluminal particles (gravitons). We show that the first order relativistic correction to Newton's gravity results from a two graviton interaction.Comment: 6 pages, Honorable mention in 2009 Gravity Essay Competition, submitted IJMPD, added reference