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Press, Boston, MA", "year": "2001", "url": "", "author": [ "Pavel Exner","Timo Weidl" ], "authors": [ {"first" : "Pavel", "last" : "Exner"}, {"first" : "Timo", "last" : "Weidl"} ], "pages": "437--443", "mrnumber" : "1883337", "mrclass" : "81Q10 (35J10 35P15)", "mrreviewer" : "Günter Berger", "bibtexKey": "MR1883337" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2f47f251990b9280b3f0ddddf1ed72328/elkepeter", "tags" : [ "iadm","Kennedy","Laplacians","Lang","quantum","graph" ], "intraHash" : "f47f251990b9280b3f0ddddf1ed72328", "interHash" : "002810b89f26ce8985d6810f83206ff3", "label" : "On the eigenvalues of quantum graph Laplacians with large complex δ couplings.", "user" : "elkepeter", "description" : "", "date" : "2021-10-08 19:32:58", "changeDate" : "2021-10-13 11:54:00", "count" : 2, "pub-type": "article", "journal": "Portugaliae Mathematica. A Journal of the Portuguese Mathematical Society", "year": "2020", "url": "", "author": [ "James B. Kennedy","Robin Lang" ], "authors": [ {"first" : "James B.", "last" : "Kennedy"}, {"first" : "Robin", "last" : "Lang"} ], "volume": "77","number": "2","pages": "133-161","abstract": "\"The authors study eigenvalues of the Laplacian (the negative second derivative operator) of a compact metric graph equipped with complex δ-vertex conditions. More precisely:\r\n(a) a continuity condition is imposed at each vertex;\r\n(b) on a selected set of vertices R, the vertex conditions\r\n∑e∼vj∂∂νf|e(vj)+αjf(vj)=0\r\nare imposed, where the interaction strengths αj are complex parameters and the derivative is taken in the direction towards the vertex; and\r\n(c) on the vertices in ∖R, Kirchhoff vertex conditions are imposed.\r\n\r\n The main focus in this article is on the asymptotic behavior of the (purely discrete) spectrum as certain coefficients αj tend to ∞ in the complex plane. If m of these coefficients tend to infinity within some sector in the open left half-plane while the remaining coefficients tend to infinity in a way such that Reαj remains bounded from below, then the authors show that exactly m eigenvalues diverge away from the positive real semi-axis. Moreover, they provide the asymptotics of these eigenvalues; the leading term is quadratic in the αj, with a coefficient depending on the vertex degrees. \r\n As variational principles are not available for the study of such non-self-adjoint problems, the authors use a Birman-Schwinger type characterization of eigenvalues in terms of a parameter-dependent Dirichlet-to-Neumann matrix (or Titchmarsh-Weyl function). In addition, they also obtain estimates for the numerical range and the eigenvalues.\"", "language" : "English", "bibtexKey": "kennedy2020eigenvalues" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/20d93a927f06d8d65321882fdeb4cd3ad/elkepeter", "tags" : [ "Quantum","iadm","Efimov","Systems","Effect","Bitter" ], "intraHash" : "0d93a927f06d8d65321882fdeb4cd3ad", "interHash" : "c156bf886d705529afa92b665fc414b4", "label" : "Virtual levels of multi-particle quantum systems and their implications for the Efimov effect", "user" : "elkepeter", "description" : "", "date" : "2021-10-08 19:16:40", "changeDate" : "2021-10-13 11:54:00", "count" : 3, "pub-type": "phdthesis", "address":"Stuttgart", "year": "2020", "url": "", "author": [ "Andreas Bitter" ], "authors": [ {"first" : "Andreas", "last" : "Bitter"} ], "supervisorgnd" : "1095129147", "language" : "eng", "eventdate" : "2020-12-18", "supervisor" : "Weidl, Timo", "doi" : "10.18419/opus-11315", "bibtexKey": "bitter2020virtual" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/24ffea2310033ddac3ec52d77b210ba8a/elkepeter", "tags" : [ "iadm","graphs","Lang","quantum","Robin","Laplacian" ], "intraHash" : "4ffea2310033ddac3ec52d77b210ba8a", "interHash" : "1d9d3866bfc31d5f2d0217f6177e7cc4", "label" : "On the eigenvalues of the non-self-adjoint Robin Laplacian on bounded domains and compact quantum graphs.", "user" : "elkepeter", "description" : "", "date" : "2021-10-08 19:15:23", "changeDate" : "2021-10-13 11:54:00", "count" : 3, "pub-type": "phdthesis", "address":"Stuttgart", "year": "2021", "url": "", "author": [ "Robin Lang" ], "authors": [ {"first" : "Robin", "last" : "Lang"} ], "supervisorgnd" : "1095129147", "language" : "English", "eventdate" : "2020-12-01", "supervisor" : "Weidl, Timo", "doi" : "10.18419/opus-11428", "bibtexKey": "lang2021eigenvalues" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2b4f7ef1c13d98c5a4e16460a93adf72f/hermann", "tags" : [ "computing","quantum" ], "intraHash" : "b4f7ef1c13d98c5a4e16460a93adf72f", "interHash" : "09441ac9463c2738e92f9f12aa192faf", "label" : "Quantum Computing verstehen", "user" : "hermann", "description" : "", "date" : "2018-06-25 14:32:21", "changeDate" : "2018-06-25 12:32:21", "count" : 1, "pub-type": "book", "publisher":"Springer Fachmedien Wiesbaden","address":"Wiesbaden", "year": "2015", "url": "", "author": [ "Matthias Homeister" ], "authors": [ {"first" : "Matthias", "last" : "Homeister"} ], "isbn" : "978-3-658-10454-2", "doi" : "10.1007/978-3-658-10455-9", "bibtexKey": "homeister2015quantum" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/24b6ca6df24e56abdcb1e84854d8137e5/hermann", "tags" : [ "computing","soc2018","quantum" ], "intraHash" : "4b6ca6df24e56abdcb1e84854d8137e5", "interHash" : "2f7ba87c2d96eaa70f55b28c8c90aa13", "label" : "Quantum Computing in the NISQ era and beyond", "user" : "hermann", "description" : "[1801.00862] Quantum Computing in the NISQ era and beyond", "date" : "2018-06-25 11:39:51", "changeDate" : "2018-06-26 07:29:48", "count" : 1, "pub-type": "misc", "year": "2018", "url": "http://arxiv.org/abs/1801.00862", "author": [ "John Preskill" ], "authors": [ {"first" : "John", "last" : "Preskill"} ], "note": "cite arxiv:1801.00862Comment: 22 pages. Based on a Keynote Address at Quantum Computing for Business, 5 December 2017. (v2) Minor corrections","abstract": "Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the\r\nnear future. Quantum computers with 50-100 qubits may be able to perform tasks\r\nwhich surpass the capabilities of today's classical digital computers, but\r\nnoise in quantum gates will limit the size of quantum circuits that can be\r\nexecuted reliably. NISQ devices will be useful tools for exploring many-body\r\nquantum physics, and may have other useful applications, but the 100-qubit\r\nquantum computer will not change the world right away --- we should regard it\r\nas a significant step toward the more powerful quantum technologies of the\r\nfuture. Quantum technologists should continue to strive for more accurate\r\nquantum gates and, eventually, fully fault-tolerant quantum computing.", "bibtexKey": "preskill2018quantum" } ] }