An alternative construction of the positive inner product for pseudo-Hermitian Hamiltonians: Examples

This paper builds on our earlier proposal for construction of a positive inner product for pseudo-Hermitian Hamiltonians and we give several examples to clarify our method. We show through the example of the harmonic oscillator how our construction applies equally well to Hermitian Hamiltonians which form a subset of pseudo-Hermitian systems. For finite dimensional pseudo-Hermitian matrix Hamiltonians we construct the positive inner product (in the case of $2\times 2$ matrices for both real as well as complex eigenvalues). When the quantum mechanical system cannot be diagonalized exactly, our construction can be carried out perturbatively and we develop the general formalism for such a perturbative calculation systematically (for real eigenvalues). We illustrate how this general formalism works out in practice by calculating the inner product for a couple of ${\cal PT}$ symmetric quantum mechanical theories.Comment: 9 pages, revte

The Impact of Participation in Cooperatives on the Success of Small Farms

This study identifies and analyzes factors that contribute to the success of small farms. Particular attention is given to the effect of participation in marketing and supply cooperatives on the success of small farms. Using modified net farm income per dollar of assets and operator’s labor and management income as measures of success, results show participation in marketing and supply cooperatives is positively correlated with success. Further, analysis findings indicate farm size, controlling for variable and fixed costs, type of ownership, management strategies used, working off the farm, and age of the operator are important factors that influence profitability (modified net farm income per dollar of assets and operator’s labor and management income) and success.cooperatives, management strategies, marketing, small farms, success, supply cooperative, Agribusiness, Marketing,

Perfect quantum transport in arbitrary spin networks

Spin chains have been proposed as wires to transport information between distributed registers in a quantum information processor. Unfortunately, the challenges in manufacturing linear chains with engineered couplings has hindered experimental implementations. Here we present strategies to achieve perfect quantum information transport in arbitrary spin networks. Our proposal is based on the weak coupling limit for pure state transport, where information is transferred between two end-spins that are only weakly coupled to the rest of the network. This regime allows disregarding the complex, internal dynamics of the bulk network and relying on virtual transitions or on the coupling to a single bulk eigenmode. We further introduce control methods capable of tuning the transport process and achieve perfect fidelity with limited resources, involving only manipulation of the end-qubits. These strategies could be thus applied not only to engineered systems with relaxed fabrication precision, but also to naturally occurring networks; specifically, we discuss the practical implementation of quantum state transfer between two separated nitrogen vacancy (NV) centers through a network of nitrogen substitutional impurities.Comment: 5+7 page

Aharonov-Bohm effect in a Class of Noncommutative Theories

The Aharonov-Bohm effect including spin-noncommutative effects is considered. At linear order in $\theta$, the magnetic field is gauge invariant although spatially strongly anisotropic. Despite this anisotropy, the Schr\"odinger-Pauli equation is separable through successive unitary transformations and the exact solution is found. The scattering amplitude is calculated and compared with the usual case. In the noncommutative Aharonov-Bohm case the differential cross section is independent of $\theta$.Comment: 10 page

Architecture of autonomous systems

Automation of Space Station functions and activities, particularly those involving robotic capabilities with interactive or supervisory human control, is a complex, multi-disciplinary systems design problem. A wide variety of applications using autonomous control can be found in the literature, but none of them seem to address the problem in general. All of them are designed with a specific application in mind. In this report, an abstract model is described which unifies the key concepts underlying the design of automated systems such as those studied by the aerospace contractors. The model has been kept as general as possible. The attempt is to capture all the key components of autonomous systems. With a little effort, it should be possible to map the functions of any specific autonomous system application to the model presented here

Mirrorless optical bistability in a nonlinear absorbing dielectric film

The optical transmissivity of a mirrorless, nonlinear, absorbing dielectric thin film is investigated numerically. The dielectric function in the film region is dependent on the intensity of the electromagnetic field. Multivalued solutions of transmissivity as a function of incident power are calculated for the steady-state wave equation. The numerical solution is applied to two different model dielectric functions. As the absorption parameter is increased, larger values of incident intensity are required to switch the systems between stable output states. Also, the peak values of transmissivity are reduced as the absorption is increased