Linear response theory of open systems with exceptional points.

Area of Science:

• Quantum mechanics
• Non-Hermitian systems
• Mathematical physics

Background:

• Linear response theory is crucial for analyzing system dynamics and stability.
• Non-Hermitian Hamiltonian systems present challenges due to non-orthogonal eigenmodes and exceptional points (EPs).

Purpose of the Study:

• To derive a closed-form series expansion for the resolvent of non-Hermitian systems.
• To investigate the impact of input and output channel selection on lineshape scaling.
• To explore tunable response behaviors near exceptional points.

Main Methods:

• Derivation of a closed-form series expansion for the resolvent using ordinary and generalized eigenfunctions.
• Analysis of lineshape scaling based on input (excitation) and output (collection) profiles.
• Demonstration of response behavior in configurations with M-th order exceptional points.

Main Results:

• A novel closed-form series expansion of the resolvent for arbitrary non-Hermitian systems is presented.
• Lineshape scaling in non-Hermitian systems is shown to be dependent on the choice of input and output channels.
• Exceptional points of order M can lead to Lorentzian or super-Lorentzian responses (order M_s = 2, 3, ..., M) based on channel selection.

Conclusions:

• The study uncovers a previously overlooked feature of non-Hermitian systems: tunable lineshape scaling.
• This work provides a new perspective on controlling the response properties of non-Hermitian systems by manipulating excitation and detection channels.
• The findings offer potential for designing novel quantum devices and sensing applications leveraging exceptional points.