Topological properties of Berry's phase

Abstract

By using a second quantized formulation of level crossing, which does not assume adiabatic approximation, a convenient formula for geometric terms including off-diagonal terms is derived. The analysis of geometric phases is reduced to a simple diagonalization of the Hamiltonian in the present formulation. If one diagonalizes the geometric terms in the infinitesimal neighborhood of level crossing, the geometric phases become trivial for any finite time interval $T$. The topological interpretation of Berry's phase such as the topological proof of phase-change rule thus fails in the practical Born-Oppenheimer approximation, where a large but finite ratio of two time scales is involved.

9 pages. A new reference was added, and the abstract and the presentation in the body of the paper have been expanded and made more precise

References in corpus (2)

• Off-Diagonal Geometric Phases
• Observation of off-diagonal geometric phase in polarized neutron interferometer experiments

Cited by in corpus (14)

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• Geometric phases and hidden local gauge symmetry
• Quantum anomaly and geometric phase; their basic differences
• Geometric phases for mixed states and decoherence
• Adiabatic approximation in the second quantized formulation
• Observation of Topological and Parity-dependent Phase of $m=0$ Spin States
• Geometric phases, gauge symmetries and ray representation
• No anomalous canonical commutators induced by Berry's phase
• Topology change from a monopole to a dipole in Berry's phase
• Berry's phase and chiral anomalies
• Is it possible to determine unambiguously the Berry phase solely from quantum oscillations?
• Geometric phase and chiral anomaly; their basic differences