General Theory of the Zitterbewegung

Details General Theory of the Zitterbewegung General Theory of the Zitterbewegung

2009-09-10

arxiv.org/abs/0909.2004v3

Phys. Rev. B 81, 121417(R) (2010)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

10 pages, no figure

Scientific paper

10.1103/PhysRevB.81.121417

We derive a general and simple expression for the time-dependence of the position operator of a multi-band Hamiltonian with arbitrary matrix elements depending only on the momentum of the quasi-particle. Our result shows that in such systems the Zitterbewegung like term related to a trembling motion of the quasi-particle, always appears in the position operator. Moreover, the Zitterbewegung is, in general, a multi-frequency oscillatory motion of the quasi-particle. We derive a few different expressions for the amplitude of the oscillatory motion including that related to the Berry connection matrix. We present several examples to demonstrate how general and versatile our result is.

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