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Abstract
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.
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.
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1 Michigan Technological University, Department of Physics, Houghton, USA (GRID:grid.259979.9) (ISNI:0000 0001 0663 5937); Michigan Technological University, Henes Center for Quantum Phenomena, Houghton, USA (GRID:grid.259979.9) (ISNI:0000 0001 0663 5937)
2 Humboldt-Universität zu Berlin, Institut für Physik, AG Theoretische Optik & Photonik, Berlin, Germany (GRID:grid.7468.d) (ISNI:0000 0001 2248 7639); Max-Born-Institut, Berlin, Germany (GRID:grid.419569.6) (ISNI:0000 0000 8510 3594)
3 University of Central Florida, CREOL/College of Optics and Photonics, Orlando, USA (GRID:grid.170430.1) (ISNI:0000 0001 2159 2859)
4 The Pennsylvania State University, Department of Engineering Science and Mechanics, and Materials Research Institute, University Park, USA (GRID:grid.29857.31) (ISNI:0000 0001 2097 4281)