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- Title
On the evolution of the semi-classical Wigner function in higher dimensions.
- Authors
S. FILIPPAS; G. N. MAKRAKIS
- Abstract
The limit Wigner measure of a WKB function satisfies a simple transport equation in phase-space and is well suited for capturing oscillations at scale of order $O(\epsilon)$, but it fails, for instance, to provide the correct amplitude on caustics where different scales appear. We define the semi-classical Wigner function of an $N$-dimensional WKB function, as a suitable formal approximation of its scaled Wigner function. The semi-classical Wigner function is an oscillatory integral that provides an $\epsilon$-dependent regularization of the limit Wigner measure, it obeys a transport-dispersive evolution law in phase space, and it is well defined even at simple caustics.
- Subjects
WIGNER distribution; WKB approximation; OSCILLATIONS; AMPLITUDE modulation; PHASE space
- Publication
European Journal of Applied Mathematics, 2006, Vol 17, Issue 1, p33
- ISSN
0956-7925
- Publication type
Article
- DOI
10.1017/s0956792505006303