Experimental identification of the second-order non-Hermitian skin effect with physics-graph-informed machine learning
Ce ShangShuo LiuRuiwen ShaoPeng HanXiaoning ZangXiangliang ZhangK. SalámaWenlong GaoChing Hua LeeRonny ThomaleAurélien ManchonShuang ZhangTie Jun CuiUdo Schwingenschlögl
2
Citation
0
Reference
10
Related Paper
Citation Trend
Abstract:
Topological phases of matter are conventionally characterized by the bulk-boundary correspondence in Hermitian systems: The topological invariant of the bulk in $d$ dimensions corresponds to the number of $(d-1)$-dimensional boundary states. By extension, higher-order topological insulators reveal a bulk-edge-corner correspondence, such that $n$-th order topological phases feature $(d-n)$-dimensional boundary states. The advent of non-Hermitian topological systems sheds new light on the emergence of the non-Hermitian skin effect (NHSE) with an extensive number of boundary modes under open boundary conditions. Still, the higher-order NHSE remains largely unexplored, particularly in the experiment. We introduce an unsupervised approach -- physics-graph-informed machine learning (PGIML) -- to enhance the data mining ability of machine learning with limited domain knowledge. Through PGIML, we experimentally demonstrate the second-order NHSE in a two-dimensional non-Hermitian topolectrical circuit. The admittance spectra of the circuit exhibit an extensive number of corner skin modes and extreme sensitivity of the spectral flow to the boundary conditions. The violation of the conventional bulk-boundary correspondence in the second-order NHSE implies that modification of the topological band theory is inevitable in higher dimensional non-Hermitian systems.Keywords:
Topological insulator
Cite
Citations (1)
In this paper, we discuss how role of interior, exterior and boundary in M-topology is different from that of similar concepts in general topology. In general topology, we have numerous results relating interior, closure, and boundary of a subset and we can characterize open sets, closed sets and clopen sets in terms of these concepts. It is shown that similar results need not be true in M- topology, and further analyses the situations for which the results are true and establishes some.
Closure (psychology)
Cite
Citations (1)
Cite
Citations (33)
Non-Hermitian systems with specific forms of Hamiltonians can exhibit novel phenomena. However, it is difficult to study their quantum thermodynamical properties. In particular, the calculation of work statistics can be challenging in non-Hermitian systems due to the change of state norm. To tackle this problem, we modify the two-point measurement method in Hermitian systems. The modified method can be applied to non-Hermitian systems which are Hermitian before and after the evolution. In Hermitian systems, our method is equivalent to the two-point measurement method. When the system is non-Hermitian, our results represent a projection of the statistics in a larger Hermitian system. As an example, we calculate the work statistics in a non-Hermitian Su-Schrieffer-Heeger model. Our results reveal several differences between the work statistics in non-Hermitian systems and the one in Hermitian systems.
Hermitian function
Cite
Citations (8)
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.
Cite
Citations (0)
The abstract boundary construction of Scott and Szekeres provides a 'boundary' for any n-dimensional, paracompact, connected, Hausdorff, C∞ manifold. Singularities may then be defined as objects within this boundary. In a previous paper (Barry R A and Scott S M 2011 Class. Quantum Grav. 28 165003), a topology referred to as the attached point topology was defined for a manifold and its abstract boundary, thereby providing us with a description of how the abstract boundary is related to the underlying manifold. In this paper, a second topology, referred to as the strongly attached point topology, is presented for the abstract boundary construction. Whereas the abstract boundary was effectively disconnected from the manifold in the attached point topology, it is very much connected in the strongly attached point topology. A number of other interesting properties of the strongly attached point topology are considered, each of which support the idea that it is a very natural and appropriate topology for a manifold and its abstract boundary.
Manifold (fluid mechanics)
Paracompact space
Digital topology
Spacetime topology
Closed manifold
Cite
Citations (4)
Cite
Citations (0)
Cite
Citations (76)
Cite
Citations (4)