Observable effects of the quantum adiabatic phase for noncyclic evolution

It is pointed out that, contrary to naive expectation, the gauge structure or Berry connection recently found in slowly varying quantum systems gives rise to observable effects even for noncyclic evolutions corresponding to open paths in parameter space. We propose to test such effects in muon spin resonance and in level-crossing resonance in muon-spin-rotation spectroscopy. In our proposals either the probe or the system itself has a lifetime much shorter than the period of one adiabatic cycle.