Abstract
It is well-known [1] that during the cyclic adiabatic evolution multi-level (quantum) system acquires the geometric phase factor, or Berry’s phase. B.Simon has shown [2] that it is precisely the holonomy in a Hermitian line bundle since the adiabatic theorem naturally defines a connection in such a bundle. In the case of degenerated systems this factor is non-Abelian [3].
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References
Berry, M.V.: Proc. R. Soc. A 392 (1984) 45.
Simon, B.: Phys. Rev. Lett. 51 (1983) 2167.
Wilchek, F., Zee, A.: Phys. Rev. Lett. 52 (1984) 2111.
Pletyukhov, M., Tolkachev, E.: J. Phys.A 32(1999) 1073.
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Pletyukhov, M.V., Tolkachev, E.A. (2000). Geometry of 2-Fold Degenerated 2-Level System. In: Gausterer, H., Pittner, L., Grosse, H. (eds) Geometry and Quantum Physics. Lecture Notes in Physics, vol 543. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46552-9_22
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DOI: https://doi.org/10.1007/3-540-46552-9_22
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