By using the method of Helffer and Sj"ostrand to construct Moyal projections, we extend the almost invariant subspace theory to the semiclassical context. Applications to the semiclassical limit for two component Klein-Gordon hamiltonian are given. More precisely, under the conditions that the potential is analytic and its eigenvalues never cross weprove that the scattering matrix is block diagonal up to exponentially small errors. Also, we show how the existence of almost invariant subspaces leads to the existence of quasi-modes with exponentially long life-times.

Semiclassical limit for multistate Klein-Gordon systems: almost invariant subspaces and scattering theory

SORDONI, VANIA
2004

Abstract

By using the method of Helffer and Sj"ostrand to construct Moyal projections, we extend the almost invariant subspace theory to the semiclassical context. Applications to the semiclassical limit for two component Klein-Gordon hamiltonian are given. More precisely, under the conditions that the potential is analytic and its eigenvalues never cross weprove that the scattering matrix is block diagonal up to exponentially small errors. Also, we show how the existence of almost invariant subspaces leads to the existence of quasi-modes with exponentially long life-times.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11585/5255
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