Symplectic inverse spectral theory for pseudodifferential operators

2008/08/21 by San Vu Ngoc, Ngoc, San Vu
Mathematics · Physics and Astronomy · #34L20 #37J35 #57R45 #58J50 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #Symplectic Geometry (math.SG) #math-ph #math.MP #math.SG #math.SP #msc:34L20 #msc:37J35 #msc:57R45 #msc:58J50

paper · pdf · doi:10.48550/arxiv.0808.2862

23 pages

arxiv created 2008/08/21 · arxiv updated 2009/12/01

Abstract

We prove, under some generic assumptions, that the semiclassical spectrum modulo O(h²) of a one dimensional pseudodifferential operator completely determines the symplectic geometry of the underlying classical system. In particular, the spectrum determines the hamiltonian dynamics of the principal symbol.

Related

• Symplectic spectral geometry of semiclassical operators
• Symplectic invariants of semitoric systems and the inverse problem for\n quantum systems
• The inverse spectral problem for quantum semitoric systems
• Etudes for the inverse spectral problem
• Eigenvalues and subelliptic estimates for non-selfadjoint semiclassical operators with double characteristics