Imperial College London

Dr H F Jones

Faculty of Natural SciencesDepartment of Physics

Distinguished Research Fellow



+44 (0)20 7594 7830h.f.jones Website




Mrs Graziela De Nadai-Sowrey +44 (0)20 7594 7843




509Huxley BuildingSouth Kensington Campus






BibTex format

author = {Jones, HF},
doi = {10.1007/s10773-014-2432-y},
journal = {International Journal of Theoretical Physics},
pages = {3986--3990},
title = {Singular mapping for a PT-Symmetric sinusoidal optical lattice at the symmetry-breaking threshold},
url = {},
volume = {54},
year = {2014}

RIS format (EndNote, RefMan)

AB - A popular PT-symmetric optical potential (variation of the refractive index) thatsupports a variety of interesting and unusual phenomena is the imaginary exponential, thelimiting case of the potential V0[cos(2πx/a) + iλ sin(2πx/a)] as λ → 1, the symmetrybreakingpoint. For λ < 1, when the spectrum is entirely real, there is a well-known mappingby a similarity transformation to an equivalent Hermitian potential. However, as λ → 1,the spectrum, while remaining real, contains Jordan blocks in which eigenvalues and thecorresponding eigenfunctions coincide. In this limit the similarity transformation becomessingular. Nonetheless, we show that the mapping from the original potential to its Hermitiancounterpart can still be implemented; however, the inverse mapping breaks down. We alsoilluminate the role of Jordan associated functions in the original problem, showing that theymap onto eigenfunctions in the associated Hermitian problem.
AU - Jones,HF
DO - 10.1007/s10773-014-2432-y
EP - 3990
PY - 2014///
SN - 1572-9575
SP - 3986
TI - Singular mapping for a PT-Symmetric sinusoidal optical lattice at the symmetry-breaking threshold
T2 - International Journal of Theoretical Physics
UR -
UR -
UR -
VL - 54
ER -