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Sánchez Soto, Luis Lorenzo and Monzón Serrano, Juan José (2018) The geometrical basis of PT symmetry. Symmetry, 10 (10). ISSN 2073-8994
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Creative Commons Attribution. 623kB |
Official URL: http://dx.doi.org/10.3390/sym10100494
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https://www.mdpi.com | Publisher |
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.
Item Type: | Article |
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Additional Information: | © 2018 by the authors. Licensee MDPI, Basel, Switzerland |
Uncontrolled Keywords: | Non-hermitian hamiltonians; Complex periodic potentials; Quantum-mechanics; Pt-symmetry; Eigenvalues; Equivalent; Scattering; Spectra |
Subjects: | Sciences > Physics > Optics |
ID Code: | 50675 |
Deposited On: | 11 Jan 2019 17:47 |
Last Modified: | 16 Jan 2019 09:55 |
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