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Physicists have succeeded in measuring geometric properties of energy bands in light crystals.
 

Geometrical phases occur in many places in nature. One of the simplest examples is the Foucault pendulum: a tall pendulum free to swing in any vertical plane. Due to Earth's rotation, the actual plane of swing rotates relative to Earth. One observes that every day the plane of rotation changes by a small "geometric" angle, associated to the spherical shape of Earth. In quantum mechanics a similar effect was discovered in 1984 by the British physicist Sir Michael Berry, who identified a geometrical phase in quantum-mechanical problems that is today known as the "Berry's phase." Such quantum-mechanical phases can have a profound effect on material properties and are responsible for a variety of phenomena. Some examples are the dielectric polarization or the quantum Hall effect, with the latter one being used nowadays to define the standard of resistance. For the first time, scientists in the group of Professor Immanuel Bloch (Ludwig-Maximilians-University, Munich and Max-Planck-Institute of Quantum Optics, Garching) in close collaboration with theoretical physicists from Harvard University in the group of Professor Eugene Demler have succeeded in measuring such a phase in a one dimensional solid-state like system. This phase is known as the "Zak-phase" named after the Israeli physicist Joshua Zak.

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