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Coherent State Path Integral for Bloch Particle

Junya Shibata·Komajiro Niizeki
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Abstract

We construct a coherent state path integral formalism for the one-dimensional Bloch particle within the single band model. The transition amplitude between two coherent states is a sum of transition amplitudes with different winding numbers on the two-dimensional phase space which has the same topology as that of the cylinder. Appearance of the winding number is due to the periodicity of the quasi-momentum of the Bloch particle. Our formalism is successfully applied to a semiclassical motion of the Bloch particle under a uniform electric field. The wave packet exhibits not only the Bloch oscillation but also a similar breathing to the one for the squeezed state of a harmonic oscillator.

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Junya Shibata, Komajiro Niizeki. 2001-05-23. Coherent State Path Integral for Bloch Particle. https://doi.org/10.1063/1.1416489

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