Fractional recurrence in discrete-time quantum walk

Quantum recurrence theorem holds for quantum systems with discrete energy eigenvalues and fails to hold in general for systems with continuous energy. We show that during quantum walk process dominated by interference of amplitude corresponding to different paths fail to satisfy the complete quantum recurrence theorem. Due to the revival of the fractional wave packet, a fractional recurrence characterized using quantum P\'olya number can be seen.Comment: 10 pages, 11 figure : Accepted to appear in Central European Journal of Physic

Coherent states for exactly solvable potentials

A general algebraic procedure for constructing coherent states of a wide class of exactly solvable potentials e.g., Morse and P{\"o}schl-Teller, is given. The method, {\it a priori}, is potential independent and connects with earlier developed ones, including the oscillator based approaches for coherent states and their generalizations. This approach can be straightforwardly extended to construct more general coherent states for the quantum mechanical potential problems, like the nonlinear coherent states for the oscillators. The time evolution properties of some of these coherent states, show revival and fractional revival, as manifested in the autocorrelation functions, as well as, in the quantum carpet structures.Comment: 11 pages, 4 eps figures, uses graphicx packag

Enabling technologies for Enterprise Wide Optimization

Current research in Enterprise Wide Optimization (EWO) is oriented more towards studying the interface between chemical engineering and operations research. This investigation studies the role of industrial automation and data mining for leveraging EWO. In particular, the role of field device integration (FDI), data models, OPC Unified Architecture (OPC UA) and information models that promote vertical data integration, and data mining techniques that create knowledge from aggregated data in enhancing EWO is studied. Further, the investigation shows that, integrating data mining and optimization models in EWO results in more realistic optimization problem that encapsulate the disturbance and uncertainties faced by process industries. As a result, EWO integrated with data mining techniques lead to more realistic solutions that are capable of dealing with uncertainties. Two illustrative examples from a rolling industry on energy and asset optimization are studied in this investigation. Our study reveals that emerging models in industrial automation and data mining are the key enablers of EWO in process industries