Self-adjoint extensions of bipartite Hamiltonians

Lenz, Daniel; Weinmann, Timon; Wirth, Melchior

Self-adjoint extensions of bipartite Hamiltonians

Lenz D, Weinmann T, Wirth M. 2021. Self-adjoint extensions of bipartite Hamiltonians. Proceedings of the Edinburgh Mathematical Society. 64(3), 443–447.

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https://doi.org/10.1017/S0013091521000080 [Published Version]

DOI

10.1017/S0013091521000080

Journal Article | Published | English

Scopus indexed

Author

Lenz, Daniel; Weinmann, Timon; Wirth, Melchior^ISTA

Department

Maas Group

Abstract

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.

Publishing Year

2021

Date Published

2021-08-01

Journal Title

Proceedings of the Edinburgh Mathematical Society

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.

Volume

Issue

Page

443-447

ISSN

0013-0915

eISSN

1464-3839

IST-REx-ID

9627

Cite this

Lenz D, Weinmann T, Wirth M. Self-adjoint extensions of bipartite Hamiltonians. Proceedings of the Edinburgh Mathematical Society. 2021;64(3):443-447. doi:10.1017/S0013091521000080

Lenz, D., Weinmann, T., & Wirth, M. (2021). Self-adjoint extensions of bipartite Hamiltonians. Proceedings of the Edinburgh Mathematical Society. Cambridge University Press. https://doi.org/10.1017/S0013091521000080

Lenz, Daniel, Timon Weinmann, and Melchior Wirth. “Self-Adjoint Extensions of Bipartite Hamiltonians.” Proceedings of the Edinburgh Mathematical Society. Cambridge University Press, 2021. https://doi.org/10.1017/S0013091521000080.

D. Lenz, T. Weinmann, and M. Wirth, “Self-adjoint extensions of bipartite Hamiltonians,” Proceedings of the Edinburgh Mathematical Society, vol. 64, no. 3. Cambridge University Press, pp. 443–447, 2021.

Lenz D, Weinmann T, Wirth M. 2021. Self-adjoint extensions of bipartite Hamiltonians. Proceedings of the Edinburgh Mathematical Society. 64(3), 443–447.

Lenz, Daniel, et al. “Self-Adjoint Extensions of Bipartite Hamiltonians.” Proceedings of the Edinburgh Mathematical Society, vol. 64, no. 3, Cambridge University Press, 2021, pp. 443–47, doi:10.1017/S0013091521000080.

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