A Stark future for quantum control

We present an overview of developments using the nonresonant dynamic Stark effect within the fields of time-resolved molecular dynamics and quantum control, drawing on examples from our own recent work. Particular emphasis is placed on the notion that "dynamics" and "control" are not distinct disciplines and that a clear synergy exits between these areas which has, up to now, been somewhat underexploited. The dynamic Stark effect is a universal interaction which we expect to have broad applicability.     

Synthesis of nanosized silver colloids by microwave dielectric heating

Silver nanosized crystallites have been synthesized in aqueous and polyols viz., ethylene glycol and glycerol, using a microwave technique. Dispersions of colloidal silver have been prepared by the reduction of silver nitrate both in the presence and absence of stabilizer poly(vinylpyrolidone) (PVP). It was observed that PVP is capable of complexing and stabilizing Ag nanoparticles formed through the reduction of Ag⁺ ions in water and ethylene glycol. In the case of ethylene glycol, it has been shown that the use of PVP leads to particles with a high degree of stability. The colloids are stable in glycerol for months even in the absence of stabilizer.     

A probabilistic inventory model for deteriorating items with lead time equal to one scheduling period

A probabilistic inventory model for continuously deteriorating items is developed, in which the lead time is assumed to be of one scheduling period, shortages are not allowed, time is treated as discrete variable, and deterioration is assumed to be a constant fraction of the on hand inventory. The developed model is related to the EOQ model for deteriorating items. An example is given to illustrate the derived results.     

Quantum geometry from coordinate transformations relating quantum observers

The relativity principle that the law of propagation for light has the same form for all macroscopic observers is extended to include quantum observers; i.e., observers who may be large, but not infinitely large, by comparison with quantum mechanical systems. This leads to the extension of the covariance group from the diffeomorphisms to the conservation group (which is the largest group of coordinate transformations under which conservation laws are covariant statements) and, thus, to the quantum geometry and quantum unified field theory considered in a previous paper.     

Nonlinear Filtering in Rieznnnnifln Manifolds

A general formulation of the nonlinear filtering problem inRiemanman manifolds is given by use of the strong solutionsof the stochastic differential equations for the state and observationprocesses in the orthonormal frame bundles of the state andobservation process manifolds, respectively. A general Bayesformula for the conditional expectation of smooth functionsof the state process is given. This is used to give a directderivation of the Zakai equation for the general problem underconsideration. An example is presented.