Quantum Gross Laplacian and Applications

Habib Ouerdiane; Samah Horrigue

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arXiv · 0804.3938

Quantum Gross Laplacian and Applications

Habib Ouerdiane·Samah Horrigue

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Abstract

In this paper, we introduce and study a noncommutative extension of the Gross Laplacian, called quantum Gross Laplacian. Then, applying the quantum Gross Laplacian to the particular case where the operator is the multiplication operator, we find a relation between classical and quantum Gross Laplacian. As application, we give explicit solution of linear quantum white noise differential equation. In particular, we give a explicit solution of the quantum Gross heat equation.

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Habib Ouerdiane, Samah Horrigue. 2008-04-24. Quantum Gross Laplacian and Applications. https://arxiv.org/abs/0804.3938

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