The Spectrum of the Hamiltonian with a PT-symmetric Periodic Optical Potential

Abstract

We give a complete description, provided with a mathematical proof, of the shape of the spectrum of the Hill operator with a PT-symmetric periodic optical potential. We prove that the second critical point, after which the real parts of the first and second bands disappear, is a number between 0.8884370025 and 0.8884370117. Moreover we prove that it is the degeneration point for the first periodic eigenvalue. Besides, we give a scheme by which one can find arbitrary precise value of the second critical point as well as the k-th critical points after which the real parts of the (2k-3)th and (2k-2)th bands disappear, where k=3,4,...

References in corpus (3)

• A note on the PT-invariant periodic potential V(x)=4 cos^2 x + 4 i V_0 sin 2x
• On the spectral properties of the Schrodinger operator with a periodic PT-symmetric potential
• On the Simplicity of the Eigenvalues of the Non-self-adjoint Mathieu-Hill Operators

Cited by in corpus (1)

• Spectral Analysis of the Schrodinger Operator with an Optical Potential