Mukunda, N. ; Arvind, ; Chaturvedi, S. ; Simon, R. (2001) Bargmann invariants and off-diagonal geometric phases for multilevel quantum systems: a unitary-group approach Physical Review A, 65 (1). 012102_1-012102_10. ISSN 1050-2947
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Official URL: http://pra.aps.org/abstract/PRA/v65/i1/e012102
Related URL: http://dx.doi.org/10.1103/PhysRevA.65.012102
Abstract
We investigate the geometric phases and the Bargmann invariants associated with multilevel quantum systems. In particular, we show that a full set of "gauge-invariant" objects for an n-level system consists of n geometric phases and 1/2(n-1)(n-2) algebraically independent four-vertex Bargmann invariants. In the process of establishing this result, we develop a canonical form for U(n) matrices that is useful in its own right. We show that the recently discovered "off-diagonal" geometric phases [N. Manini and F. Pistolesi, Phys. Rev. Lett. 8, 3067 (2000)] can be completely analyzed in terms of the basic building blocks developed in this work. This result liberates the off-diagonal phases from the assumption of adiabaticity used in arriving at them.
Item Type: | Article |
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Source: | Copyright of this article belongs to American Physical Society. |
ID Code: | 7006 |
Deposited On: | 26 Oct 2010 04:40 |
Last Modified: | 16 May 2016 17:15 |
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