A transformation property of the Wigner distribution under Hamiltonian symplectomorphisms

被引：4
|
作者：
de Gosson, Maurice [1 ]
机构：
[1] Univ Vienna, NuHAG, Fac Math, A-1090 Vienna, Austria
来源：
JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS | 2011年 / 2卷 / 01期
基金：
奥地利科学基金会;
关键词：
Hamiltonian Function; Canonical Transformation; Wigner Distribution; Weyl Operator; Linear Canonical Transformation;
D O I：
10.1007/s11868-011-0023-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove an exact symplectic covariance formula under nonlinear Hamiltonian phase flows (f(t)(H)) 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[f(t)(H) (Z)] = W psi(t).
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页码：91 / 99
页数：9
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