General theory of Zitterbewegung

We derive a general and simple expression for the time dependence of the position operator of a multiband Hamiltonian with arbitrary matrix elements depending only on the momentum of the quasiparticle. Our result shows that in such systems the Zitterbewegung-type term related to a trembling motion of the quasiparticle, always appears in the position operator. Moreover, the Zitterbewegung is, in general, a multifrequency oscillatory motion of the quasiparticle. We derive a few alternative 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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