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Observable Dirac-type singularities in Berry's phase and the monopole.
1Raman Research Institute, Bangalore 560 080, India. bhandari@rri.res.in
Physical Review Letters
|March 23, 2002
Summary
Adiabatic cycles of spin-1/2 wave functions encircling a degeneracy result in a +/-2pi phase shift. This principle extends to interferometers around magnetic monopoles, yielding observable +/-2npi phase shifts.
Area of Science:
- Quantum mechanics
- Theoretical physics
- Geometric phase
Background:
- Adiabatic cycles in quantum mechanics can lead to phase shifts.
- Spin-1/2 systems exhibit unique quantum properties.
- Degeneracies in Hamiltonian parameter space are critical points.
Purpose of the Study:
- To generalize the sign-change rule for adiabatic cycles in 3D.
- To investigate phase shifts resulting from looping degeneracies.
- To explore implications for magnetic monopole interactions.
Main Methods:
- Three-dimensional generalization of adiabatic cycle theory.
- Analysis of wave function phase shifts.
- Theoretical modeling of interferometer loops around magnetic monopoles.
Main Results:
- A Dirac-type singularity arises from looping degeneracies.
- Observable +/-2pi phase shifts are predicted for adiabatic cycles.
- Interferometer loops around magnetic monopoles yield +/-2npi phase shifts.
Conclusions:
- The study provides a generalized understanding of geometric phases in quantum systems.
- The findings have implications for quantum interferometry and the study of magnetic monopoles.
- The +/-2npi phase shift is a fundamental observable related to topology.