Spectral Rigidity for Periodic Schrödinger Operators in Dimension 2

Abstract

We consider two dimensional real-valued analytic potentials for the Schrödinger equation which are periodic over a lattice $L$. Under certain assumptions on the form of the potential and the lattice $L$, we can show there is a large class of analytic potentials which are Floquet rigid and dense in the set of $C^{\infty }(R^2/L)$ potentials. The result extends the work of Eskin et. al, in "On isospectral periodic potentials in $R^n$, II."

published version may differ,Annales de l'Institut Henri Poincare (c) nonlinear analysis (2014)

References in corpus (2)

• On the negative spectrum of two-dimensional Schrödinger operators with radial potentials
• Dispersion for Schrödinger Operators with One-gap Periodic Potentials on R^1

Cited by in corpus (1)

• Gauge Equivalence and the Inverse Spectral Problem for the Magnetic Schrödinger Operator on the Torus