Non-Hermitian Dynamics without all-to-all Coupling in Odd-Channel Systems

Yıl 2024, Cilt: 7 Sayı: 2, 179 - 183, 30.11.2024

Ege Özgün

https://doi.org/10.34088/kojose.1434585

Öz

Here we analytically derive the eigenspectra of non-Hermitian systems with an odd number of channels in a scheme that eliminates the requirement of all-to-all coupling of the channels. The calculated spectrum displays coexisting parity-time broken and parity-time symmetric modes for any choice of coupling and gain/loss values except for the case of N=3 where a certain range of coupling and gain/loss parameters are required for the coexistence of parity-time broken and parity-time symmetric modes.

Anahtar Kelimeler

Discrete Symmetries, Mode Coupling, Non-Hermitian Physics, Parity-Time Symmetry

Kaynakça

• [1] Bender C. M., Boettcher S., 1998. Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry. Physical Review Letters, 80(24), pp. 5243-5246
• [2] Mostafazadeh A., 2002. Pseudo-Hermiticity versus symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian. Journal of Mathematical Physics, 43(1) pp. 205-214
• [3] El-Ganainy R., Makris K. G., Christodoulides D. N. and Musslimani Z. H., 2007. Theory of coupled optical PT-symmetric structures. Optics Letters, 32(17), pp. 2632-2634
• [4] Makris K. G., El-Ganainy R. and Christodoulides D. N., 2008. Beam Dynamics in PT Symmetric Optical Lattices. Physical Review Letters, 100, 103904.
• [5] Rüter C. E., Makris K. G., El-Ganainy R., Christodoulides D. N., Segev M. and Kip D., 2010. Observation of parity–time symmetry in optics. Nature Physics, 6 pp. 192-195
• [6] Guo A., Salamo G. J., Duchesne D., Morandotti R., Volatier-Ravat M., Aimez V., Siviloglou G. A. and Christodoulides D. N., 2009. Observation of PT-Symmetry Breaking in Complex Optical Potentials. Physical Review Letters, 103 093902
• [7] Ge L., Chong Y. D. and Stone A. D., 2012. Conservation relations and anisotropic transmission resonances in one-dimensional PT-symmetric photonic heterostructures Physical Review A, 85 023802.
• [8] Sounas D. L., Fleury R. and Alù A., 2015. Unidirectional cloaking based on metasurfaces with balanced loss and gain. Physical Review Applied, 4 014005.
• [9] Chitsazi M., Li H., Ellis F. M. and Kottos T., 2017. Experimental Realization of Floquet PT- Symmetric Systems. Physical Review Letters, 119, 093901
• [10] Yuce C., 2015. PT symmetric Floquet topological phase. The European Physical Journal D, 69(184) pp. 1-5
• [11] Klaiman S., Günther U. and Moiseyev N., 2008.Visualization of Branch Points in PT-Symmetric Waveguides. Physical Review Letters, 101 080402.
• [12] Feng L., Wong Z. J., Ma R.-M., Wang Y. and Zhang X., 2014. Single-mode laser by parity-time symmetry breaking. Science, 346(6212) pp. 972-975
• [13] Özgün E., Serebryannikov A. E., Ozbay E. and Soukoulis C. M., 2017. Broadband mixing of PT-symmetric and PT-broken phases in photonic heterostructures with a one-dimensional loss/gain bilayer. Scientific Reports, 7 15504
• [14] Özgün E. and Hakioğlu T. and Ozbay E., 2020. Scattering of Spin-1/2 Particles from a PT-symmetric Complex Potential. EPL, 131 11001.
• [15] Özgün E., Ozbay E. and Ozdur I., 2022. Four-channel parity-time symmetry. EPL, 140 10001
• [16] Özgün E., 2023. N-channel Parity-time symmetry. EPL, 144 30002
• [17] Zhang J. and Yao J., 2018. Parity-time–symmetric optoelectronic oscillator. Science Advances, 4 eaar678