Abstract
The versatile and exactly solvable Scarf II potential has been predicting, confirming and demonstrating interesting phenomena in complex PT-symmetric sector, most impressively. However, for the non-PT-symmetric sector, it has gone underutilised. Here, we present the most simple analytic forms for the scattering coefficients \((T(k),R(k),|\det S(k)|)\). On the one hand, these forms demonstrate earlier effects and confirm the recent ones. On the other hand, they make new predictions – all simple and analytical. We show the possibilities of both self-dual and non-self-dual spectral singularities (NSDSS) in two non-PT sectors (potentials). The former one is not accompanied by time-reversed coherent perfect absorption (CPA) and gives rise to the parametrically controlled splitting of spectral singularity (SS) into a finite number of complex conjugate pairs of eigenvalues (CCPEs). NSDSS behave just oppositely: CPA but no splitting of SS. We demonstrate a one-sided reflectionlessness without invisibility. Most importantly, we bring out a surprising coexistence of both real discrete spectrum and a single SS in a fixed potential. Nevertheless, so far, the complex Scarf II potential is not known to be pseudo-Hermitian (\(\eta ^{-1} H\eta =H^\dagger \)) under a metric of the type \(\eta (x)\).
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References
L Gendenshtein, JETP Lett. 38, 356 (1983)
C M Bender and S Boettcher, Phys. Rev. Lett. 80, 5243 (1998)
B Bagchi and R Roychowdhury, J. Phys. A 33, L1 (2000)
Z Ahmed, Phys. Lett. A 282, 343 (2001)
A Khare and U P Sukhatme, J. Phys. A 21, L501 (1988)
Z Ahmed, Phys. Rev. A 64, 042716 (2001)
Z Ahmed, Phys. Lett. A 324, 152 (2004)
A Mostafazadeh, Phys. Rev. Lett. 102, 220402 (2009)
Z Ahmed, J. Phys. A 42, 472005 (2009)
B Bagchi and C Quesne, J. Phys. A 43, 395301 (2010)
Y D Chong, L Ge, H Cao and A D Stone, Phys. Rev. Lett. 105, 053901 (2010)
S Longhi, Phys. Rev. A 81, 022102 (2010)
Y D Chong, Li Ge and A D Stone, Phys. Rev. Lett. 106, 093902 (2011)
A Mostafazadeh, J. Phys. A 45, 444024 (2012)
Z Ahmed, J. Phys. A 45, 032004 (2012)
V V Konotop and D A Zezyulin, Opt. Lett. 42, 5206 (2017)
Z Ahmed, S Kumar and D Ghosh, Phys. Rev. A 98, 042101 (2018)
D A Zezyulin and V V Konotop, New J. Phys. 22, 013057 (2020)
V V Konotop, E Lashtanov and B Vainberg, Phys. Rev. A 99, 043838 (2019)
A Mostafazadeh, Phys. Rev. A 87, 012103 (2013)
B Midya, Phys. Rev. A 89, 032116 (2014)
Z Ahmed, J. Phys. A 42, 485303 (2014)
Z Ahmed and J A Nathan, Phys. Lett. A 379, 865 (2015)
A Mostafazadeh, J. Math. Phys. 43, 286; 43, 2814 (2002)
Z Ahmed, Phys. Lett. A 290, 19 (2001); 294, 287 (2002)
T V Fityo, J. Phys. A 35, 5813 (2002)
C Hang, G Gabadadze and G Huang, Phys. Rev. A 95, 023833 (2017)
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Kumar, S., Ahmed, Z. An update on coherent scattering from complex non-PT-symmetric Scarf II potential with new analytic forms. Pramana - J Phys 95, 63 (2021). https://doi.org/10.1007/s12043-021-02089-x
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DOI: https://doi.org/10.1007/s12043-021-02089-x
Keywords
- Non-Hermitian potential
- coherent scattering
- coherent perfect absorption
- lasing
- spectral singularity
- real
- complex conjugate
- single non-real eigenvalue