Non-Hermitian systems are physical systems whose effective Hamiltonians or dynamical generators are not equal to their Hermitian conjugates, leading to complex eigenvalues and non-orthogonal eigenstates. They naturally model open, dissipative, or gain–loss systems where energy or probability is not conserved, such as in photonics, acoustics, and cold-atom platforms. Non-Hermitian systems exhibit distinctive phenomena including exceptional points, non-Hermitian skin effects, and modified bulk–boundary correspondence, often described using biorthogonal bases. They are analyzed via non-Hermitian extensions of quantum and wave theories, with particular attention to spectral properties, stability, and the role of symmetries such as parity–time (PT) symmetry.
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