PT symmetry and Weyl asymptotics
Johannes Sjoestrand
TL;DR
This paper demonstrates that PT-symmetric operators with small random perturbations typically follow Weyl asymptotics, leading to numerous non-real eigenvalues when the principal symbol is non-real.
Contribution
It establishes probabilistic Weyl asymptotics for PT-symmetric operators under small random perturbations, revealing the prevalence of non-real eigenvalues.
Findings
Eigenvalues follow Weyl asymptotics with high probability
Presence of many non-real eigenvalues when principal symbol is non-real
Results apply to a class of PT-symmetric operators
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.
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Taxonomy
TopicsQuantum Mechanics and Non-Hermitian Physics · Terahertz technology and applications · Quantum chaos and dynamical systems