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Spectral monodromy of small non-selfadjoint quantum perturbations of completely integrable Hamiltonians
- Source :
- Journal of Mathematical Analysis and Applications. 458:795-811
- Publication Year :
- 2018
- Publisher :
- Elsevier BV, 2018.
-
Abstract
- We define a monodromy, directly from the spectrum of small non-selfadjoint perturbations of a selfadjoint semiclassical operator with two degrees of freedom, which is classically integrable. It is a combinatorial invariant that obstructs globally the existence of lattice structure of the spectrum, in the semiclassical limit. Moreover this spectral monodromy allows to recover a topological invariant (the classical monodromy) of the corresponding integrable system.<br />18 pages, 1 figure. arXiv admin note: text overlap with arXiv:1405.3930
- Subjects :
- Integrable system
Applied Mathematics
Operator (physics)
010102 general mathematics
Spectrum (functional analysis)
Semiclassical physics
01 natural sciences
35P20, 81Q12
Mathematics - Analysis of PDEs
Monodromy
0103 physical sciences
FOS: Mathematics
010307 mathematical physics
Limit (mathematics)
0101 mathematics
Invariant (mathematics)
Mathematics::Symplectic Geometry
Quantum
Analysis
Analysis of PDEs (math.AP)
Mathematics
Mathematical physics
Subjects
Details
- ISSN :
- 0022247X
- Volume :
- 458
- Database :
- OpenAIRE
- Journal :
- Journal of Mathematical Analysis and Applications
- Accession number :
- edsair.doi.dedup.....8ac5a273a3a81340cd9003e8f1edec65