The discussion centers on the Berry's phase in the context of Bloch oscillations, specifically questioning whether the phase acquired by the wavefunction of an electron can be nontrivial. It is established that while Bloch oscillations involve the wavefunction returning to its initial state after a period, the phase can indeed be nontrivial under certain conditions. The participants clarify that a periodic potential alone does not lead to a Berry phase; rather, it is the dependence of the Hamiltonian on parameters that are varied along a closed path in parameter space that gives rise to the Berry phase.
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wdlang said:we know in bloch oscillation, the wavefunction of an electron returns to its initial state after a period, but up to a phase.
my question is, can this phase be nontrivial?