Linear response theory of open systems with exceptional points

A. Hashemi, K. Busch, D. N. Christodoulides, S. K. Ozdemir, R. El-Ganainy

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


Understanding the linear response of any system is the first step towards analyzing its linear and nonlinear dynamics, stability properties, as well as its behavior in the presence of noise. In non-Hermitian Hamiltonian systems, calculating the linear response is complicated due to the non-orthogonality of their eigenmodes, and the presence of exceptional points (EPs). Here, we derive a closed form series expansion of the resolvent associated with an arbitrary non-Hermitian system in terms of the ordinary and generalized eigenfunctions of the underlying Hamiltonian. This in turn reveals an interesting and previously overlooked feature of non-Hermitian systems, namely that their lineshape scaling is dictated by how the input (excitation) and output (collection) profiles are chosen. In particular, we demonstrate that a configuration with an EP of order M can exhibit a Lorentzian response or a super-Lorentzian response of order Ms with Ms = 2, 3, …, M, depending on the choice of input and output channels.

Original languageEnglish (US)
Article number3281
JournalNature communications
Issue number1
StatePublished - Dec 2022

All Science Journal Classification (ASJC) codes

  • General Chemistry
  • General Biochemistry, Genetics and Molecular Biology
  • General Physics and Astronomy


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