Spectral asymptotics via the semiclassical Birkhoff normal form

Simple item page
dc.creatorCharles, Laurent
dc.creatorNgoc, San Vu
dc.date2006-05-03
dc.date.accessioned2026-07-07T12:40:03Z
dc.date.available2026-07-07T12:40:03Z
dc.descriptionThis article gives a simple treatment of the quantum Birkhoff normal form for semiclassical pseudo-differential operators with smooth coefficients. The normal form is applied to describe the discrete spectrum in a generalised non-degenerate potential well, yielding uniform estimates in the energy $E$. This permits a detailed study of the spectrum in various asymptotic regions of the parameters $(E,\h)$, and gives improvements and new proofs for many of the results in the field. In the completely resonant case we show that the pseudo-differential operator can be reduced to a Toeplitz operator on a reduced symplectic orbifold. Using this quantum reduction, new spectral asymptotics concerning the fine structure of eigenvalue clusters are proved. In the case of polynomial differential operators, a combinatorial trace formula is obtained.
dc.description44 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/math/0605096
dc.identifierhttp://arxiv.org/abs/math/0605096
dc.identifierDuke Mathematical Journal 143, 3 (2008) 463--511
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/219329
dc.subjectSpectral Theory
dc.subjectMathematical Physics
dc.subject58J40, 58J50, 58K50, 47B35, 53D20
dc.titleSpectral asymptotics via the semiclassical Birkhoff normal form
dc.typetext

Files

Collections

arXiv