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A transformation property of the Wigner distribution under Hamiltonian symplectomorphisms

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Abstract

We prove an exact symplectic covariance formula under nonlinear Hamiltonian phase flows (f H t ) for the Wigner distribution \({W\psi}\) . A key role is played in our derivation by the linearized flow at the point where the Wigner distribution is calculated. We show that in general there does not exist any function \({\psi_{t}}\) such that \({W\psi\lbrack f_{t}^{H}(z)]=W\psi_{t}}\).

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Authors and Affiliations

  1. Faculty of Mathematics, NuHAG, University of Vienna, Nordbergstraß e 15, 1090, Vienna, Austria

    Maurice de Gosson

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  1. Maurice de Gosson
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Correspondence to Maurice de Gosson.

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de Gosson, M. A transformation property of the Wigner distribution under Hamiltonian symplectomorphisms. J. Pseudo-Differ. Oper. Appl. 2, 91–99 (2011). https://doi.org/10.1007/s11868-011-0023-8

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  • DOI: https://doi.org/10.1007/s11868-011-0023-8

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