TOPOLOGICAL PROPERTIES OF BERRY'S PHASE
2005 ◽
Vol 20
(05)
◽
pp. 335-343
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Keyword(s):
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.
1988 ◽
Vol 21
(7)
◽
pp. 1595-1599
◽
1994 ◽
Vol 195
(5-6)
◽
pp. 296-300
◽
Keyword(s):
1998 ◽
Vol 100
(3)
◽
pp. 665-670
◽
2012 ◽
Vol 2012
◽
pp. 1-17
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2004 ◽
Vol 41
(2)
◽
pp. 570-578
◽