Imaginary parts of Stark–Wannier resonances

DOI10.1063/1.532406zbMath1001.34075OpenAlexW1967385492MaRDI QIDQ4260496

Alain Grigis, Vladimir S. Buslaev

Publication date: 15 December 2002

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.532406

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) General spectral theory of ordinary differential operators (34L05) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) (2)-body potential quantum scattering theory (81U05)

Related Items

On the mathematical work of Vladimir Savel′evich Buslaev ⋮ Monodromization method in the theory of almost-periodic equations ⋮ Adiabatic asymptotics of reflection coefficients of a quantum electron moving in a two-dimensional waveguide ⋮ Complex WKB method (one-dimensional linear problems on the complex plane) ⋮ Stark-Wannier ladders and cubic exponential sums ⋮ Adiabatic asymptotics of the reflection coefficient ⋮ Complex WKB method for adiabatic perturbations of a periodic Schrödinger operator ⋮ Turning points for adiabatically perturbed periodic equations ⋮ Wannier-Stark resonances in optical and semiconductor superlattices ⋮ Spacing gain and absorption in a simple $ \newcommand{\PT}{\mathcal{PT}} \PT$ -symmetric model: spectral singularities and ladders of eigenvalues and resonances

Cites Work

• Adiabatic perturbation of a periodic potential
• Existence of Stark ladder resonances
• Adiabatic theorem and spectral concentration. I: Arbitrary order spectral concentration for the Stark effect in atomic physics
• Stark Wannier ladders
• Stark ladder resonances for small electric fields
• Stark resonances in disordered systems
• Lower bounds on the width of Stark-Wannier type resonances