PT symmetry and Weyl asymptotics

2011/05/24 by Johannes Sjoestrand, Sjoestrand, Johannes
Engineering · Mathematics · Physics and Astronomy · #35P20 #FOS: Mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory (math.SP) #Terahertz technology and applications #math.SP #msc:35P20

paper · pdf · doi:10.48550/arxiv.1105.4746

arxiv created 2011/05/24 · openalex publication_date 2011/05/24 · arxiv updated 2011/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a class of PT-symmetric operators with small random perturbations, the eigenvalues obey Weyl asymptotics with probability close to 1. Consequently, when the principal symbol is non-real, there are many non-real eigenvalues.

Related

• Eigenvalue asymptotics for randomly perturbed non-selfadjoint operators
• Eigenvalue distribution for non-self-adjoint operators with small multiplicative random perturbations
• PT-symmetry and Schrödinger operators. The double well case
• Exponential asymptotics for the eigenvalues in the broken PT-symmetric region
• Eigenvalue distributions and Weyl laws for semi-classical non-self-adjoint operators in 2 dimensions