Work

Contractivity properties of a quantum diffusion semigroup

Year: 2017

Type: article

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.

Source: Journal of Mathematical Physics

DOI: 10.1063/1.4974223

Authors: Nilanjana Datta, Yan Pautrat, Cambyse Rouzé

Institutions: University of Cambridge, Université Paris-Sud, Centre National de la Recherche Scientifique, Université Paris-Saclay, Laboratoire de Mathématiques d'Orsay

Language: English

Topic: Quantum Mechanics and Applications

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funder: Agence Nationale de la Recherche

Award: Stochastic Methods in Quantum Mechanics