Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric Phases for Mixed States during Cyclic Evolutions   The geometric phases of cyclic evolutions for mixed states are discussed in
the framework of unitary evolution. A canonical one-form is defined whose line
integral gives the geometric phase which is gauge invariant. It reduces to the
Aharonov and Anandan phase in the pure state case. Our definition is consistent
with the phase shift in the proposed experiment [Phys. Rev. Lett. \textbf{85},
2845 (2000)] for a cyclic evolution if the unitary transformation satisfies the
parallel transport condition. A comprehensive geometric interpretation is also
given. It shows that the geometric phases for mixed states share the same
geometric sense with the pure states.

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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph