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Quantum Lévy Laplacian and associated heat equation |
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| Authors: | Un Cig Ji Nobuaki Obata Habib Ouerdiane |
| Institution: | a Department of Mathematics, Research Institute of Mathematical Finance, Chungbuk National University, Cheongju 361-763, Republic of Korea b Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan c Département de Mathématiques, Faculté de Sciences de Tunis, Université de Tunis El Manar, Campus Universitaire, Tunis 1060, Tunisia |
| Abstract: | As a non-commutative extension of the Lévy Laplacian for entire functions on a nuclear space, we define the quantum Lévy Laplacian acting on white noise operators. We solve a heat type equation associated with the quantum Lévy Laplacian and study its relation to the classical Lévy heat equation. The solution to the quantum Lévy heat equation is obtained also from a normal-ordered white noise differential equation involving the quadratic quantum white noise. |
| Keywords: | Quantum Lé vy Laplacian Heat equation Quantum white noise Wick symbol White noise operator |
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