Linear response theory of open systems with exceptional points

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-orthogona...

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Bibliographic Details
Published in:Nature communications 2022-06, Vol.13 (1), p.3281-3281, Article 3281
Main Authors: Hashemi, A., Busch, K., Christodoulides, D. N., Ozdemir, S. K., El-Ganainy, R.
Format: Article
Language:English
Subjects:
639/624/400/385
639/766/400/1021
Configurations
Dynamic stability
Dynamical systems
Eigenvectors
Exact solutions
Hamiltonian functions
Humanities and Social Sciences
Light
Mathematical analysis
multidisciplinary
Nonlinear dynamics
Nonlinear systems
Open systems
Optics
Orthogonality
Science
Science (multidisciplinary)
Series expansion
Spectral sensitivity
Stability analysis
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Summary: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 M s with M s  = 2, 3, …,  M , depending on the choice of input and output channels. The authors develop a closed-form expansion of the linear response associated with resonant non-Hermitian systems having exceptional points and demonstrate that the spectral response may involve different super Lorentzian lineshapes depending on the input/output channel configuration.
ISSN:2041-1723
2041-1723
DOI:10.1038/s41467-022-30715-8