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arXiv · 1607.04242

Contractivity properties of a quantum diffusion semigroup

Nilanjana Datta·Yan Pautrat·Cambyse Rouze
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Abstract

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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Nilanjana Datta, Yan Pautrat, Cambyse Rouze. 2016-07-14. Contractivity properties of a quantum diffusion semigroup. https://doi.org/10.1063/1.4974223

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