The authors define Riesz and generalized density matrices for non-Hermitian Hamiltonians and use them to track purity and entropy near exceptional points.
Christensen, An Introduction to Frames and Riesz Bases , Birkh¨ auser, Boston, (2003) 24
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Density matrices and entropy operator for non-Hermitian quantum mechanics
The authors define Riesz and generalized density matrices for non-Hermitian Hamiltonians and use them to track purity and entropy near exceptional points.