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Non-Hermitian Hamiltonians provide an alternative perspective on the dynamics of quantum and classical systems coupled non-conservatively to an environment. Once primarily an interest of mathematical physicists, the theory of non-Hermitian Hamiltonians has solidified and expanded to describe various physically observable phenomena in optical, photonic, and condensed matter systems. Self-consistent descriptions of quantum mechanics based on non-Hermitian Hamiltonians have been developed and continue to be refined. In particular, non-Hermitian frameworks to describe magnonic and hybrid magnonic systems have gained popularity and utility in recent years with new insights into the magnon topology, transport properties, and phase transitions coming into view. Magnonic systems are in many ways a natural platform in which to realize non-Hermitian physics because they are always coupled to a surrounding environment and exhibit lossy dynamics. In this Perspective, we review recent progress in non-Hermitian frameworks to describe magnonic and hybrid magnonic systems, such as cavity magnonic systems and magnon–qubit coupling schemes. We discuss progress in understanding the dynamics of inherently lossy magnetic systems as well as systems with gain induced by externally applied spin currents. We enumerate phenomena observed in both purely magnonic and hybrid magnonic systems which can be understood through the lens of non-Hermitian physics, such as PT and anti-PT-symmetry breaking, dynamical magnetic phase transitions, non-Hermitian skin effect, and the realization of exceptional points and surfaces. Finally, we comment on some open problems in the field and discuss areas for further exploration.
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Resolvent expansion for discrete non-Hermitian resonant systems [Invited]
The linear response of non-Hermitian resonant systems demonstrates various intriguing features such as the emergence of non-Lorentzian lineshapes. Recently, we have developed a systematic theory to understand the scattering lineshapes in such systems and, in doing so, established the connection with the input/output scattering channels. Here, we follow up on that work by presenting a different, more transparent derivation of the resolvent operator associated with a non-Hermitian system under general conditions and highlight the connection with the structure of the underlying eigenspace decomposition. Finally, we also present a simple solution to the problem of self-orthogonality associated with the left and right Jordan canonical vectors and show how the left basis can be constructed in a systematic fashion. Our work provides a unifying mathematical framework for studying non-Hermitian systems such as those implemented using dielectric cavities, metamaterials, and plasmonic resonators.
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- PAR ID:
- 10386636
- Publisher / Repository:
- Optical Society of America
- Date Published:
- Journal Name:
- Optical Materials Express
- Volume:
- 13
- Issue:
- 1
- ISSN:
- 2159-3930
- Format(s):
- Medium: X Size: Article No. 229
- Size(s):
- Article No. 229
- Sponsoring Org:
- National Science Foundation
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