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The Geometrical Basis of PT Symmetry

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Sanchez-Soto,  Luis
Quantumness, Tomography, Entanglement, and Codes, Leuchs Division, Max Planck Institute for the Science of Light, Max Planck Society;
Complutense University of Madrid;

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Citation

Sanchez-Soto, L., & Monzon, J. J. (2018). The Geometrical Basis of PT Symmetry. SYMMETRY-BASEL, 10(10): 494. doi:10.3390/sym10100494.


Cite as: http://hdl.handle.net/21.11116/0000-0003-F39E-9
Abstract
We reelaborate on the basic properties of PT symmetry from a geometrical perspective. The transfer matrix associated with these systems induces a Mobius transformation in the complex plane. The trace of this matrix classifies the actions into three types that represent rotations, translations, and parallel displacements. We find that a PT invariant system can be pictured as a complex conjugation followed by an inversion in a circle. We elucidate the physical meaning of these geometrical operations and link them with measurable properties of the system.