The asymptotics of the gap in the Mathieu equation

DOI10.1016/0003-4916(81)90005-1zbMath0464.34020OpenAlexW2021190545MaRDI QIDQ1154030

Joseph E. Avron, Barry Simon

Publication date: 1981

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

Full work available at URL: https://doi.org/10.1016/0003-4916(81)90005-1

zbMATH Keywords

tunneling in momentum space

Mathematics Subject Classification ID

General theory of ordinary differential operators (47E05) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30) Ordinary differential operators (34L99)

Related Items (34)

Interchanging space and time in nonlinear optics modeling and dispersion management models ⋮ Asymptotics of instability zones of Hill operators with a two term potential ⋮ Adiabatic invariants and asymptotic behavior of Lyapunov exponents of the Schrödinger equation ⋮ Isospectral Mathieu-Hill operators ⋮ Twelve tales in mathematical physics: An expanded Heineman prize lecture ⋮ Intervalles d'instabilité pour une équation de Hill à potentiel méromorphe ⋮ Asymptotics of instability zones of the Hill operator with a two term potential ⋮ Band gap of the spectrum in periodically curved quantum waveguides ⋮ Instability intervals and growth rates for Hill’s equation ⋮ Numerical finite-gap integration of the Zabusky–Kruskal problem ⋮ Instanton solutions on the polymer harmonic oscillator ⋮ Hill's potentials in weighted Sobolev spaces and their spectral gaps ⋮ WKB and resurgence in the Mathieu equation ⋮ Estimations asymptotiques des intervalles d'instabilité pour l'équation de Hill ⋮ Spectral gaps of the periodic Schrödinger operator when its potential is an entire function. ⋮ Refined asymptotics of the spectral gap for the Mathieu operator ⋮ Almost periodic Schrödinger operators. I: Limit periodic potentials ⋮ Spectral triangles of non-selfadjoint Hill and Dirac operators ⋮ Energy splitting in dynamical tunneling ⋮ Free vibration of a class of Hill's equations having a small parameter ⋮ Multiplicities of the eigenvalues of periodic Dirac operators ⋮ Critical Lieb-Thirring bounds in gaps and the generalized Nevai conjecture for finite gap Jacobi matrices ⋮ On the estimations of the small periodic eigenvalues ⋮ On the instability intervals of the Mathieu--Hill operator ⋮ The Mathieu differential equation and generalizations to infinite fractafolds ⋮ Instability intervals of the Ince and Hill equations ⋮ Unnamed Item ⋮ The complex side of the TS/ST correspondence ⋮ On the instability tongues of the Hill equation coupled with a conservative nonlinear oscillator ⋮ Simple and double eigenvalues of the Hill operator with a two-term potential ⋮ Cantor spectrum for the almost Mathieu equation ⋮ Charged particles in an intense, plane electromagnetic wave: Limitations of the nonrelativistic theory ⋮ Riesz basis property of Hill operators with potentials in weighted spaces ⋮ Smoothness of Schrödinger operator potential in the case of Gevrey type asymptotics of the gaps.

Cites Work

• Double wells
• On the rate of asymptotic eigenvalue degeneracy
• The band-structure of a one-dimensional, periodic system in a scaling limit
• The inverse problem for periodic potentials
• Instability intervals of Hill's equation
• Estimates on the Stability Intervals for Hill's Equation
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The asymptotics of the gap in the Mathieu equation