It is common to calculate Berry phases for quantum systems in, for example, a magnetic field. In this case we compute the Berry phase ##\gamma## using(adsbygoogle = window.adsbygoogle || []).push({});

$$\gamma[C] = i\oint_C \! \langle n,t| \left( \vec{\nabla}_R |n,t\rangle \right)\,\cdot{d\vec{R}} \,$$

where ##R## parametrizes the cyclic adiabatic process, in this case, the magnetic field.

I was wondering what the Berry phase is for a system that has no external fields. Say, you have a particle in a box and the box rotates in three-dimensional box about some point. How do you compute the Berry phase for this system?

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# I Berry phase without a magnetic field

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