Origin of branch points in the spectrum ofPT-symmetric periodic potentials

2009/08/24 by Ching-Hao Chang, Ching‐Hao Chang, Shi-Ming Wang +1
Mathematics · Physics and Astronomy · #Algorithm #Amplitude #Bifurcation #Combinatorics #Eigenvalues and eigenvectors #Mathematics #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Spectrum (functional analysis) #cond-mat.other #quant-ph

paper · pdf · doi:10.1103/physreva.80.042105

6 pages, 5figures

arxiv created 2009/08/24 · openalex publication_date 2009/10/06 · arxiv updated 2015/05/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

There exist multiple branch points in the energy spectrum for some PT-symmetric periodic potentials, where the real eigenvalues turn into complex ones. By studying the transmission amplitude for a localized complex potential, we elucidate the physical origin of the breakdown of the perturbation method and Born approximation. Most importantly, we derive an analytic criterion to determine why, when, and where the bifurcation will occur.

Citations

• Reflectionless potentials and symmetry
• Making sense of non-Hermitian Hamiltonians
• Real Spectra in Non-Hermitian Hamiltonians HavingPTSymmetry
• Calculations of time-dependent observables in non-Hermitian quantum mechanics: The problem and a possible solution
• Complex Extension of Quantum Mechanics