Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Contractivity properties of a quantum diffusion semigroup   We consider a quantum generalization of the classical heat equation, and
study contractivity properties of its associated semigroup. We prove a Nash
inequality and a logarithmic Sobolev inequality. The former leads to an
ultracontractivity result. This in turn implies that the largest eigenvalue and
the purity of a state with positive Wigner function, evolving under the action
of the semigroup, decrease at least inverse polynomially in time, while its
entropy increases at least logarithmically in time.

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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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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: solv-int
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph