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1. Non-Hermitian Dynamics in a Hermitian System

   https://doi.org/10.1364/NLO.2021.NTh1A.4  

   Flemens, Noah ; Moses, Jeffrey ( January 2021 , OSA Nonlinear Optics 2021)

   Boyd, R. ; Conti, C. ; Christodoulides, D. ; Rakich, P. (Ed.)
2. Non-Hermitian Dynamics Mimicked by a Hermitian Nonlinear System

   Flemens, Noah ; Swenson, Nicolas ; Moses, Jeffrey ( January 2021 , ArXivorg)

   null (Ed.)

   We illustrate that a Hermitian nonlinear optical system consisting of hybridized parametric amplification and second harmonic generation mimics non-Hermitian evolution dynamics. Oscillation damping, evolution to a static steady state, and exceptional points arise from the use of second harmonic generation as an irreversible loss mechanism. The investigated system can be used to solve problems of inefficiency in parametric amplifier systems used widely in laser science and industrial applications. More generally, these findings suggest a new paradigm for the engineering of system dynamics where energy recovery and system sustainability are of importance. 

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3. Twisted Hermitian Codes

   https://doi.org/10.3390/math9010040  

   Allen, Austin ; Blackwell, Keller ; Fiol, Olivia ; Kshirsagar, Rutuja ; Matsick, Bethany ; Matthews, Gretchen L. ; Nelson, Zoe ( January 2021 , Mathematics)

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   We define a family of codes called twisted Hermitian codes, which are based on Hermitian codes and inspired by the twisted Reed–Solomon codes described by Beelen, Puchinger, and Nielsen. We demonstrate that these new codes can have high-dimensional Schur squares, and we identify a subfamily of twisted Hermitian codes that achieves a Schur square dimension close to that of a random linear code. Twisted Hermitian codes allow one to work over smaller alphabets than those based on Reed–Solomon codes of similar lengths. 

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4. Hermitian-lifted codes

   https://doi.org/10.1007/s10623-020-00836-6  

   López, Hiram H. ; Malmskog, Beth ; Matthews, Gretchen L. ; Piñero-González, Fernando ; Wootters, Mary ( March 2021 , Designs, Codes and Cryptography)

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5. Non-Hermitian boost deformation

   https://doi.org/10.1103/PhysRevB.108.075108  

   Guo, Taozhi ; Kawabata, Kohei ; Nakai, Ryota ; Ryu, Shinsei ( August 2023 , Physical Review B)