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Zero width resonance (spectral singularity) in a complex PT-symmetric potential

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Zafar Ahmed

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We show that the complex PT-symmetric potential V(x) = −V1 sech2x + iV2 sech xtanh x entails a single zero-width resonance (spectral singularity) when V_1 + |V_2| = 4n^2 + 4n + {3\over 4} (n=0,1,2,3,\ldots, |V_2|\gt V_1 + 1/4) and the positive resonant energy is given as E_*={1 \over 4}[|V_2|-(1/4+V_1)] .


PACS

11.30.Er Charge conjugation, parity, time reversal, and other discrete symmetries

02.40.Xx Singularity theory

02.10.Ud Linear algebra

MSC

81U20 S-matrix theory, etc.

58K70 Symmetries, equivariance

15A18 Eigenvalues, singular values, and eigenvectors

Subjects

Mathematical physics

Particle physics and field theory

Dates

Issue 47 (27 November 2009)

Received 12 August 2009, in final form 17 October 2009

Published 9 November 2009



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