Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamic process and Uhlmann process: Incompatibility and dynamic phase
  of mixed quantum states   While a pure quantum state may accumulate both the Berry phase and dynamic
phase as it undergoes a cyclic path in the parameter space, the situation is
more complicated when mixed quantum states are considered. From the Ulhmann
bundle, a mixed quantum state can accumulate the Ulhmann phase if the
parallel-transport condition is satisfied. However, we show that the Ulhmann
process is in general not compatible with the evolution equation of the density
matrix governed by the Hamiltonian. Thus, a mixed quantum state usually
accumulates a dynamic phase during its time evolution. We present the
expression of the dynamic phase for mixed quantum states. In examples of
quasi-static one-dimensional two-band models and simple harmonic oscillator,
the dynamic phase can take multiple discrete values at infinitely high
temperature due to the resonant points. However, the behavior differs if the
energy spectrum is continuous without a band gap. Moreover, there is no natural
analog of the dynamic phase in classical systems.

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The categories of this paper are: math
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat