Projective Hilbert space structures at exceptional points
作者： Uwe Günther , Ingrid Rotter , Boris F Samsonov
DOI: 10.1088/1751-8113/40/30/014
关键词: Projection-valued measure 、 Mathematical analysis 、 Rigged Hilbert space 、 Projective Hilbert space 、 Complex projective space 、 Hilbert manifold 、 SIC-POVM 、 POVM 、 Mathematics 、 Hilbert scheme
摘要: A non-Hermitian complex symmetric 2x2 matrix toy model is used to study projective Hilbert space structures in the vicinity of exceptional points (EPs). The bi-orthogonal eigenvectors a diagonalizable are Puiseux-expanded terms root vectors at EP. It shown that apparent contradiction between two incompatible normalization conditions with finite and singular behavior EP-limit can be resolved by projectively extending original space. complementary correspond then different affine charts this enlarged Geometric phase jump analyzed usefulness rigidity as measure for distance EP configurations demonstrated. Finally, EP-related aspects PT-symmetrically extended Quantum Mechanics discussed conjecture concerning quantum brachistochrone problem formulated.
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