An Extension of Gauss-Bonnet's Theorem C: Gauss-Bonnet Theorem in Non-Hermitian Systems: Skin Effect and Topological Conservation
An Extension of Gauss-Bonnet's Theorem C: Gauss-Bonnet Theorem in Non-Hermitian Systems: Skin Effect and Topological Conservation
This paper investigates the extension of the Gauss-Bonnet theorem in nonHermitian systems. By introducing the concepts of non-Hermitian curvature and boundary localization phenomena induced by the skin effect, we establish a generalized Gauss-Bonnet formula applicable to non-reciprocal systems. This formula maintains topological conservation while quantifying the impact of boundary skin effects on geometric-topological relationships through a jump index. The theoretical framework is mathematically rigorous and self-consistent, with physical applications in non-Hermitian topological photonic crystals and circuit systems, providing new theoretical tools for understanding topological phase transitions in non-reciprocal systems.
Gauss-Bonnet Theorem; Non-Hermitian Systems; Skin Effect; Topolog ical Conservation; Non-reciprocity; Curvature Renormalization; Boundary Localization; Topology-Skin Correspondence, Gauss-Bonnet Theorem; Non-Hermitian Systems; Skin Effect; Topolog ical Conservation; Non-reciprocity; Curvature Renormalization; Boundary Localization; Topology-Skin Correspondence
Gauss-Bonnet Theorem; Non-Hermitian Systems; Skin Effect; Topolog ical Conservation; Non-reciprocity; Curvature Renormalization; Boundary Localization; Topology-Skin Correspondence, Gauss-Bonnet Theorem; Non-Hermitian Systems; Skin Effect; Topolog ical Conservation; Non-reciprocity; Curvature Renormalization; Boundary Localization; Topology-Skin Correspondence
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