Zitterbewegung of Klein-Gordon particles and its simulation by classical systems

The Klein-Gordon equation is used to calculate the Zitterbewegung (ZB, trembling motion) of spin-zero particles in absence of fields and in the presence of an external magnetic field. Both Hamiltonian and wave formalisms are employed to describe ZB and their results are compared. It is demonstrated that, if one uses wave packets to represent particles, the ZB motion has a decaying behavior. It is also shown that the trembling motion is caused by an interference of two sub-packets composed of positive and negative energy states which propagate with different velocities. In the presence of a magnetic field the quantization of energy spectrum results in many interband frequencies contributing to ZB oscillations and the motion follows a collapse-revival pattern. In the limit of non-relativistic velocities the interband ZB components vanish and the motion is reduced to cyclotron oscillations. The exact dynamics of a charged Klein-Gordon particle in the presence of a magnetic field is described on an operator level. The trembling motion of a KG particle in absence of fields is simulated using a classical model proposed by Morse and Feshbach -- it is shown that a variance of a Gaussian wave packet exhibits ZB oscillations.Comment: 16 pages and 7 figure

Agile Manufacturing: an evolutionary review of practices

Academics and practitioners have long acknowledged the importance of agile manufacturing and related supply chains in achieving firm sustainable competitiveness. However, limited, if any, research has focused on the evolution of practices within agile manufacturing supply chains and how these are related to competitive performance objectives. To address this gap, we reviewed the literature on agile manufacturing drawing on evolution of manufacturing agility, attributes of agile manufacturing, the drivers of agile manufacturing, and the identification of the enabling competencies deployable for agile manufacturing. Our thesis is that agile manufacturing is at the centre of achieving sustainable competitive advantage, especially in light of current unprecedented market instability coupled with complex customer requirements. In this regard, the emphasis which agile manufacturing places on responsive adaptability would counter the destabilising influence of competitive pressures on organisations performance criteria. We have identified five enabling competencies as the agility enablers and practices of agile manufacturing, that is, transparent customisation, agile supply chains, intelligent automation, total employee empowerment and technology integration, and further explored their joint deployment to create positive multiplier effects. Future research directions were also provided with respect to operationalisation of the five identified enablers and the potential for emergent technologies of big data, blockchain, and Internet of Things to shape future agile manufacturing practices

Development of a new prototype system for measuring the permittivity of dielectric materials

A simple prototype for measuring the properties of dielectric materials is introduced in this Letter. A homogeneous dielectric sample placed in a field produced by a nearby antenna will affect the input impedance of the antenna. The permittivity and the loss of the dielectric sample can then be determined from the change of the input impedance of the antenna. The prototype has been validated by experiments