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Schlagwörter:
COMPLEX PERIODIC POTENTIALS; SYMMETRIC QUANTUM-MECHANICS; HERMITIAN
HAMILTONIANS; SPONTANEOUS BREAKDOWN; EIGENVALUES; REAL; SPECTRUMOptics; Physics;
Zusammenfassung:
We show that the transfer matrix for a PT-invariant system, when recast in the appropriate variables, can be interpreted as a point in the (3 + 1)-dimensional de Sitter space. We introduce a natural PT-invariant composition law for these matrices and confirm that their action appears as a Lorentz transformation. We elucidate the geometrical meaning of the PT symmetry breaking and suggest that the cosmological event horizon arising in the de Sitter metric can be can be unraveled with a simple optical scheme. DOI: 10.1103/PhysRevA.87.012111