Hamiltonian formulation of linear non-Hermitian systems

• URL: http://arxiv.org/abs/2309.06162v1
• Date: Tue, 12 Sep 2023 12:12:32 GMT
• Title: Hamiltonian formulation of linear non-Hermitian systems
• Authors: Qi Zhang
• Abstract summary: 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.
• Score: 7.298673108358943
• License: http://creativecommons.org/publicdomain/zero/1.0/
• 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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