Lagrangian intersections and glancing points: typical transitions of phase in semiclassical approximations

Ilya Bogaevskii; Michel Rouleux

Lagrangian intersections and glancing points: typical transitions of phase in semiclassical approximations

Mathematical Physics 2023-11-16 v1 math.MP

Authors: Ilya Bogaevskii , Michel Rouleux

Abstract

Given a semiclassical distribution $f_h$ microlocalized on a Lagrangian manifold $\Lambda_0$ , $H\in C^\infty( T^\ast {\bf R}^n)$ , and $H=E$ a regular energy surface, we find asymptotic solutions of the PDE $(H(x,\widehat{p})-E) \, u_h (x,E)=f_h(x)$ in terms of the Maslov canonical operator, when the Hamilton vector field $v_H$ fails to be transverse to $\Lambda_0$ at some points.

Keywords

semiclassical approximation lagrangian manifold maslov canonical operator hamilton vector field phase transition pde asymptotic solution

Cite

@article{arxiv.2311.08889,
  title  = {Lagrangian intersections and glancing points: typical transitions of phase in semiclassical approximations},
  author = {Ilya Bogaevskii and Michel Rouleux},
  journal= {arXiv preprint arXiv:2311.08889},
  year   = {2023}
}

Lagrangian intersections and glancing points: typical transitions of phase in semiclassical approximations

Abstract

Keywords

Cite

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