{"language":[{"iso":"eng"}],"issue":"3","doi":"10.1017/S0013091521000080","date_created":"2021-07-04T22:01:24Z","date_published":"2021-08-01T00:00:00Z","publication_status":"published","day":"01","page":"443-447","article_type":"original","oa_version":"Published Version","volume":64,"type":"journal_article","year":"2021","date_updated":"2023-08-17T07:12:05Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","_id":"9627","title":"Self-adjoint extensions of bipartite Hamiltonians","external_id":{"isi":["000721363700003"],"arxiv":["1912.03670"]},"citation":{"ista":"Lenz D, Weinmann T, Wirth M. 2021. Self-adjoint extensions of bipartite Hamiltonians. Proceedings of the Edinburgh Mathematical Society. 64(3), 443–447.","short":"D. Lenz, T. Weinmann, M. Wirth, Proceedings of the Edinburgh Mathematical Society 64 (2021) 443–447.","chicago":"Lenz, Daniel, Timon Weinmann, and Melchior Wirth. “Self-Adjoint Extensions of Bipartite Hamiltonians.” <i>Proceedings of the Edinburgh Mathematical Society</i>. Cambridge University Press, 2021. <a href=\"https://doi.org/10.1017/S0013091521000080\">https://doi.org/10.1017/S0013091521000080</a>.","apa":"Lenz, D., Weinmann, T., &#38; Wirth, M. (2021). Self-adjoint extensions of bipartite Hamiltonians. <i>Proceedings of the Edinburgh Mathematical Society</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/S0013091521000080\">https://doi.org/10.1017/S0013091521000080</a>","mla":"Lenz, Daniel, et al. “Self-Adjoint Extensions of Bipartite Hamiltonians.” <i>Proceedings of the Edinburgh Mathematical Society</i>, vol. 64, no. 3, Cambridge University Press, 2021, pp. 443–47, doi:<a href=\"https://doi.org/10.1017/S0013091521000080\">10.1017/S0013091521000080</a>.","ieee":"D. Lenz, T. Weinmann, and M. Wirth, “Self-adjoint extensions of bipartite Hamiltonians,” <i>Proceedings of the Edinburgh Mathematical Society</i>, vol. 64, no. 3. Cambridge University Press, pp. 443–447, 2021.","ama":"Lenz D, Weinmann T, Wirth M. Self-adjoint extensions of bipartite Hamiltonians. <i>Proceedings of the Edinburgh Mathematical Society</i>. 2021;64(3):443-447. doi:<a href=\"https://doi.org/10.1017/S0013091521000080\">10.1017/S0013091521000080</a>"},"oa":1,"abstract":[{"text":"We compute the deficiency spaces of operators of the form 𝐻𝐴⊗̂ 𝐼+𝐼⊗̂ 𝐻𝐵, for symmetric 𝐻𝐴 and self-adjoint 𝐻𝐵. This enables us to construct self-adjoint extensions (if they exist) by means of von Neumann's theory. The structure of the deficiency spaces for this case was asserted already in Ibort et al. [Boundary dynamics driven entanglement, J. Phys. A: Math. Theor. 47(38) (2014) 385301], but only proven under the restriction of 𝐻𝐵 having discrete, non-degenerate spectrum.","lang":"eng"}],"main_file_link":[{"url":"https://doi.org/10.1017/S0013091521000080","open_access":"1"}],"isi":1,"author":[{"first_name":"Daniel","last_name":"Lenz","full_name":"Lenz, Daniel"},{"full_name":"Weinmann, Timon","first_name":"Timon","last_name":"Weinmann"},{"id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","first_name":"Melchior","orcid":"0000-0002-0519-4241","last_name":"Wirth","full_name":"Wirth, Melchior"}],"publisher":"Cambridge University Press","publication_identifier":{"eissn":["1464-3839"],"issn":["0013-0915"]},"department":[{"_id":"JaMa"}],"month":"08","acknowledgement":"M. W. gratefully acknowledges financial support by the German Academic Scholarship Foundation (Studienstiftung des deutschen Volkes). T.W. thanks PAO Gazprom Neft, the Euler International Mathematical Institute in Saint Petersburg and ORISA GmbH for their financial support in the form of scholarships during his Master's and Bachelor's studies respectively. The authors want to thank Mark Malamud for pointing out the reference [1] to them. This work was supported by the Ministry of Science and Higher Education of the Russian Federation, agreement No 075-15-2019-1619.","article_processing_charge":"No","intvolume":"        64","publication":"Proceedings of the Edinburgh Mathematical Society","scopus_import":"1","quality_controlled":"1"}