Nonlinear Non-Hermitian Skin Effect and Skin Solitons in Temporal
Photonic Feedback Lattices
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Non-Hermitian skin effect (NHSE), i.e., the localization of eigenstates near lattice boundaries, has recently spurred tremendous interest in topological physics. Beyond the well-explored linear NHSE, the interplay of nonlinearity and skin localization represents a cutting-edge area of research, offering novel insights into wave propagation and localization control in various physical systems. Unlike the linear NHSE successfully observed in weak-power optical systems, the observation of nonlinear NHSE and resulting skin solitons remains so far elusive, mainly due to the high energy levels required in most of nonlinear effects. Here we report the experimental demonstration of nonlinear NHSE in a Kerr nonlinear temporal photonic lattice, where the high-power limitation and lack of tunability intrinsic to optical materials are overcome by an artificial nonlinearity arising from opto-electronic feedback. Thanks to Kerr self-trapping, the nonlinear NHSE is demonstrated to possess much better localization strength and robustness at the preferred boundary compared to the linear case. Away from the preferred boundary, Kerr self-trapping can even inhibit NHSE-induced transport and form stable skin solitons. Harnessing the nonlinearity-controlled NHSE, we judiciously design an optical router with a flexibly-tuned output port. Our findings promise great applications in robust signal transmission, routing, and processing.Keywords:
Skin effect
In non-Hermitian systems, the phenomenon that the bulk-band eigenstates are accumulated at the boundaries of the systems under open boundary conditions is called non-Hermitian skin effect (NHSE), which is one of the most iconic and important features of a non-Hermitian system. In this work, we investigate the fate of NHSE in the presence of electric fields by analytically calculating the dynamical evolution of an initial bulk state and numerically computing the spectral winding number, the distributions of eigenstates, as well as the dynamical evolutions. We show abundant manipulation effects of dc and ac fields on the NHSE, and that the physical mechanism behind these effects is the interplay between the Stark localization, dynamic localization and the NHSE. In addition, the finite size analysis of the non-Hermitian system with a pure dc field shows the phenomenon of size-dependent NHSE. We further propose a scheme to realize the discussed model based on an electronic circuit. The results will help to deepen the understanding of NHSE and its manipulation.
Skin effect
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We study a non-Hermitian Su-Schrieffer-Heeger model with nonreciprocal hopping under periodic driving, and show that the Floquet topological nature and non-Hermiticity can have rich interplay in this non-Hermitian Floquet topological system. We find that both the topological characteristics and the non-Hermitian skin effect are affected by the Floquet driving and can be associated with the quasienergy spectrum topology. For general choice of system and driving parameters, we derive a non-Bloch bulk-boundary correspondence to successfully describe the Floquet topological edge states with non-Hermitian skin effects. We observe interesting bipolar non-Hermitian skin effect by periodically driving the short-range non-Hermitian system, and establish its connection to the winding of Bloch quasienergy spectrum. Finally, we propose to implement the non-Hermitian quantum system with asymmetric hopping in cold atomic gases. Our work demonstrates the impact of periodic driving on non-Hermitian topological systems, and suggests a route to search for richer non-Hermitian skin effects through Floquet engineering.
Floquet theory
Skin effect
Periodic boundary conditions
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In recent years, a large number of novel phenomena such as the breakdown of conventional bulk-boundary correspondence and non-Hermitian skin effect, have emerged in non-Hermitian systems. In this work, we investigate the localization of the eigenstates and the non-Hermitian skin effect of the disordered non-Hermitian Su-Schrieffer-Heeger (SSH) model by inverse participation rate (IPR) and average inverse participation rate (MIPR). We also investigate the bulk-boundary correspondence ratio of the system. Based on the above, we further investigate the effect of disorder on the non-Hermitian skin effect and the topological properties of the NH system. We find that the disorder does not destroy the localization of the topological edge state due to the protection from the topology of the system. But the eigenstates of bulk are greatly affected by the disorder. In the presence of disorder, the eigenstates of the bulk will rapidly extend into the bulk. Thus, the non-Hermitian skin effect is vulnerable to the disorder. When the disorder is enhanced, the non-Hermitian skin effect will be greatly suppressed. We also show that the disorder will reduce the energy gap and imaginary energy of the system. Our study contributes to the further understanding of the non-Hermitian skin effect.
Skin effect
Periodic boundary conditions
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Recently, the topological phase in non-Hermitian systems has been a rapidly expanding field. The iconic features of non-Hermitian systems are exceptional points at which the eigenmodes coalesce and the non-Hermitian skin effect. We study the non-Hermitian Su-Schrieffer-Heeger model with long-range nonreciprocal hopping and find the model exhibiting topologically nontrivial phases which can be characterized by the non-Bloch winding number. With specific parameter values, the skin effect can be eliminated. As long-range nonreciprocal hopping is not easy for experimental implementations, we furthermore propose a feasible electrical-circuit simulation with operational amplifiers to implement the non-Hermitian term to realize these interesting states.
Skin effect
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In non-Hermitian systems, the phenomenon that the bulk-band eigenstates are accumulated at the boundaries of the systems under open boundary conditions is called non-Hermitian skin effect (NHSE), which is one of the most iconic and important features of a non-Hermitian system.In this work, we investigate the fate of NHSE in the presence of electric fields by analytically calculating the dynamical evolution of an initial bulk state and numerically computing the spectral winding number, the distributions of eigenstates, as well as the dynamical evolutions.We show abundant manipulation effects of dc and ac fields on the NHSE, and that the physical mechanism behind these effects is the interplay between the Stark localization, dynamic localization and the NHSE.In addition, the finite size analysis of the non-Hermitian system with a pure dc field shows the phenomenon of size-dependent NHSE.We further propose a scheme to realize the discussed model based on an electronic circuit.The results will help to deepen the understanding of NHSE and its manipulation.
Skin effect
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Білім берy қоғaмның экономикaлық дaмyының негізі, әлеyметтік тұрaқтылықтың фaкторлaрының бірі, хaлықтың рyхaни-aдaмгершілік әлеyетінің және интеллектyaлдық өсyінің қaйнaр көзі ретінде бaрлық yaқыттaрдa тaптырмaс құндылық болып есептеліп келеді. Aл қaзіргідей aдaм кaпитaлын қaлыптaстырy мен дaмытy мәселесін шешy негізгі міндет ретінде қaрaстырылaтын зaмaндa хaлықтың білімдік қaжеттіліктері өсіп, жоғaры, ортa aрнayлы, кәсіби қосымшa білім aлyғa үміткерлер сaны aртa түсyде. Бұғaн жayaп ретінде білім берy ұйымдaрының сaлaлaнyы aртып, әртүрлі типтегі оқy орындaрының сaны aртyдa, білім берyдің инфрaқұрылымы, бaсқaрy формaлaры, әдістемелік, ғылыми қызмет түрлері дaмyдa. Олaрды білім aлyшылaрдың жеке сұрaныстaры мен мүмкіндіктеріне бaғыттay күшейтілyде. Осығaн орaй білімнің сaпaсынa қойылaтын тaлaптaр aртып, бұл сaлaның әлеyметпен өзaрa әрекеттестігіне негізделген құрылымдық – қызметтік дaмyының көкейтестілігі aртyдa. Мaқaлaдa «серіктестік», «әлеyметтік серіктестік», «білімдегі әлеyметтік серіктестік» ұғым- дaрының мәні aшылып, олaрдың қaлыптaсy және дaмy үрдісіне шолy жaсaлaды, жоғaры оқy орындaрындa педaгогтaрды дaярлayдa әлеyметтік серіктестердің әлеyетін пaйдaлaнyдa бaсшылыққa aлынaтын ұстaнымдaр мен тиімді жолдaры сипaттaлaды. Түйін сөздер: серіктестік, әлеyметтік серіктестік, білімдегі әлеyметтік серіктестік, бірлескен әрекет ұстaнымдaры, әлеуметтік серіктестік әлеуеті. Обрaзовaние является основой экономического рaзвития обществa, одним из фaкторов социaль- ной стaбильности, источником дyховно-нрaвственного потенциaлa и интеллектyaльного ростa людей и во все временa считaлось незaменимой ценностью. И в нaстоящее время, когдa решение проблемы формировaния и рaзвития человеческого кaпитaлa рaссмaтривaется кaк основнaя зaдaчa, рaстyт обрaзовaтельные потребности людей, yвеличивaется количество желaющих полyчить высшее, среднее, специaльное, профессионaльное дополнительное обрaзовaние. В ответ нa это yсиливaется рaзветвленность обрaзовaтельных оргaнизaций, yвеличивaется количество обрaзовaтельных оргaни- зaций рaзличного типa, рaзвивaются инфрaстрyктyрa обрaзовaния, формы yпрaвления, методическaя и нayчнaя деятельность. Yсиливaется их ориентaция нa индивидyaльные потребности и возможности обyчaющихся. В связи с этим повышaются требовaния к кaчествy обрaзовaния, возрaстaет знaчение стрyктyрно-фyнкционaльного рaзвития этой сферы нa основе взaимодействия с обществом. В стaтье рaскрывaется знaчение понятий «пaртнерство», «социaльное пaртнерство», «социaльное пaртнерство в обрaзовaнии», рaссмaтривaется процесс их стaновления и рaзвития, описывaются рyко- водящие принципы и эффективные способы использовaния потенциaлa социaльных пaртнеров в подготовке педaгогических кaдров в высших yчебных зaведениях. Ключевые словa: партнерство, социaльное пaртнерство, социaльное пaртнерство в обрaзовaнии, принципы совместного действия, поненциал социального партнерство. Education is the basis of the economic development of society, one of the factors of social stability, a source of spiritual and moral potential and intellectual growth of people and has always been considered an irreplaceable value. And at the present time, when the solution of the problem of the formation and development of human capital is considered as the main task, the educational needs of people are growing, the number of people wishing to receive higher, secondary, special, professional additional education is increasing. In response to this, the branching of educational organizations is increasing, the number of educational organizations of various types is increasing, the infrastructure of education, forms of management, methodological and scientific activities are developing. Their focus on the individual needs and capabilities of students is increasing. In this regard, the requirements for the quality of education are increasing, the importance of the structural and functional development of this sphere on the basis of interaction with society is increasing. The article reveals the meaning of the concepts of "partnership", "social partnership", "social partnership in education", examines the process of their formation and development, describes the guidelines and effective ways to use the potential of social partners in the training of teachers in higher educational institutions. Keywords: partnership, social partnership, social partnership in education, principles of joint action, the potential of social partnership.
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The non-Hermitian skin effect is a distinctive phenomenon in non-Hermitian systems, which manifests as the anomalous localization of bulk states at the boundary. To understand the physical origin of the non-Hermitian skin effect, a bulk band characterization based on the dynamical degeneracy on an equal frequency contour is proposed, which reflects the strong anisotropy of the spectral function. In this paper, we report the experimental observation of both phenomena in a two-dimensional acoustic crystal, and reveal their remarkable correspondence by performing single-frequency excitation measurements. Our work not only provides a controllable experimental platform for studying the non-Hermitian physics, but also confirms the correspondence between the non-Hermitian skin effect and the dynamical degeneracy splitting, paving a new way to characterize the non-Hermitian skin effect.
Degeneracy (biology)
Skin effect
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The non-Hermitian skin effect is a unique phenomenon in which an extensive number of eigenstates are localized at the boundaries of a non-Hermitian system. Recent studies show that the non-Hermitian skin effect is significantly suppressed by magnetic fields. In contrast, we demonstrate that the second-order skin effect (SOSE) is robust and can even be enhanced by magnetic fields. Remarkably, SOSE can also be induced by magnetic fields from a trivial non-Hermitian system that does not experience any skin effect at zero field. These properties are intimately related to to the persistence and emergence of topological line gaps in the complex energy spectrum in the presence of magnetic fields. Moreover, we show that a magnetic field can drive a non-Hermitian system from a hybrid skin effect, where the first-order skin effect and SOSE coexist, to pure SOSE. Our results describe a qualitatively new magnetic field behavior of the non-Hermitian skin effect.Received 30 December 2022Revised 3 July 2023Accepted 16 August 2023DOI:https://doi.org/10.1103/PhysRevLett.131.116601© 2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasLocalizationTopological phases of matterPhysical SystemsNon-Hermitian systemsCondensed Matter, Materials & Applied Physics
Skin effect
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Although non-Hermitian skin effect has been discussed in periodic media having band structures, we show that continuous media can exhibit similar non-Hermitian skin effects when appropriate loss and anisotropy are incorporated.
Skin effect
Media Theory
Hermitian function
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The flourishment of non-Hermitian topology has promoted the development of skin effect, a well-known feature of the non-Hermitian systems, by which the bulk states evolve from extended to localized toward boundaries. However, in previous works, the scenarios are usually delicately designed with intricate parameters to explore the skin effects. In this work, we propose a simple paradigm to implement tunable non-Hermitian skin effects in one and two-dimensional Su-Schrieffer-Heeger (SSH)-like tight-binding models. Skin modes with distinct dimensions can be predicted irrespective of the non-Hermitian systems are topological or not. They also have no relations with the coupling values, but only are dependent on the scaling factors of non-reciprocal hopping terms. Furthermore, by engineering the hopping configurations, the skin modes could be predicted at expected edges or corners, featuring skin effects hierarchical. These tunable non-Hermitian skin effects and higher-dimensional non-Hermitian skin effects can be exploited to guide waves into targeted regions and may have useful applications when realized in metamaterials.
Skin effect
Reciprocal
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