Schrodinger differential equation leads to vanishing Berry phase

Details Schrodinger differential equation leads to vanishing Berry phase Schrodinger differential equation leads to vanishing Berry phase

2010-10-18

arxiv.org/abs/1010.3885v1

Physics

General Physics

page 5; Vanishing Berry phase would lead to inconsistency of quantum adiabatic theorem

Scientific paper

Berry phase, as a non-trivial topological effect, depends on the existence of the singularity of wave function. As a result, the wave function should be non-analytic in the adiabatic limit 1/T=0. Our study shows that if the quantum adiabatic theorem satisfies the Schrodinger differential equation in the adiabatic limit 1/T=0, then the wave function would be analytical in its definitional domain (manifold). Nevertheless, the analyticity of wave function would rule out any singularity and hence give rise to vanishing Berry phase. That means, the Schrodinger differential equation would become invalid in the adiabatic limit 1/T=0 and hence could not completely describe physical reality. However, the Schrodinger integral equation is a logical way of completely describing physical reality, since it not only is valid in common cases but also in the adiabatic limit 1/T=0.

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