6533b858fe1ef96bd12b5ba0
RESEARCH PRODUCT
Adiabatic evolution for systems with infinitely many eigenvalue crossings
Hans-rudolf JauslinStéphane GuérinF. MontiAlain Joyesubject
Rest (physics)Physics[ MATH ] Mathematics [math]Mathematical analysisSpectrum (functional analysis)FOS: Physical sciencesStatistical and Nonlinear PhysicsMathematical Physics (math-ph)Mathematics::Spectral Theory01 natural sciencesUpper and lower boundsAdiabatic theorem0103 physical sciences010307 mathematical physicsDifferentiable functionLimit (mathematics)[MATH]Mathematics [math]010306 general physicsAdiabatic processMathematical PhysicsEigenvalues and eigenvectorsdescription
International audience; We formulate an adiabatic theorem adapted to models that present an instantaneous eigenvalue experiencing an infinite number of crossings with the rest of the spectrum. We give an upper bound on the leading correction terms with respect to the adiabatic limit. The result requires only differentiability of the considered projector, and some geometric hypothesis on the local behavior of the eigenvalues at the crossings.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1998-12-23 |