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Using Kaluza-Klein theory we discuss the quantum mechanics of a particle inthe background of a domain wall (brane) embedded in extra dimensions. We showthat the geometric phases associated with the particle depend on thetopological features of those spacetimes. Using a cohomological modelingschema, we deduce a random phase sequence composed of the geometric phasesaccompanying the periodic evolution over the spacetimes. The random phasesequence is demonstrated some properties that could be experimentalverification. We argue that it is related to the nonlocality of quantumentanglement.

Random geometric phase sequence due to topological effects in our brane world from extra dimensions