Hamiltonian formulation of linear non-Hermitian systems

Qi Zhang

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arXiv · 2309.06162

Hamiltonian formulation of linear non-Hermitian systems

Qi Zhang

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Abstract

For a linear non-Hermitian system, I demonstrate that a Hamiltonian can be constructed such that the non-Hermitian equations can be expressed exactly in the form of Hamilton's canonical equations. This is first shown for discrete systems and then extended to continuous systems. With this Hamiltonian formulation, I am able to identify a conserved charge by applying Noether's theorem and recognize adiabatic invariants. When applied to Hermitian systems, all the results reduce to the familiar ones associated with the Schr\"odinger equation.

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Qi Zhang. 2023-09-12. Hamiltonian formulation of linear non-Hermitian systems. https://arxiv.org/abs/2309.06162

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