Nature of electron Zitterbewegung in crystalline solids

We demonstrate both classically and quantum mechanically that the Zitterbewegung (ZB, the trembling motion) of electrons in crystalline solids is nothing else, but oscillations of velocity assuring the energy conservation when the electron moves in a periodic potential. This means that the nature of electron ZB in a solid is completely different from that of relativistic electrons in a vacuum, as proposed by Schrodinger. Still, we show that the two-band {\bf k.p} model of electronic band structure, formally similar to the Dirac equation for electrons in a vacuum, gives a very good description of ZB in solids. Our results indicate unambiguously that the trembling motion of electrons in solids should be observable.Comment: 5 pages, 3 figure

On some inflation model based on the past price dynamics

The paper describes a model of a price movement path formed upon the past dynamics, following from a couple of assumptions. A system of delayed differential equations has been built and the properties of solutions analyzed. At the end, the main conclusions drawn from the model are presented.inflation, economic system, a delay vector, a price movement path