Self-adjoint extensions of bipartite Hamiltonians. Issue 3 (22nd August 2021)

• Record Type: Journal Article
• Authors: Lenz, Daniel; Weinmann, Timon; Wirth, Melchior
• Is Part Of: Proceedings of the Edinburgh Mathematical Society. Volume 64:Issue 3(2021)
• Page Start: 433
• Page End: 447
• Publication Date: 2021-08-22
• Subjects: operator theory -- functional analysis -- mathematical physics -- quantum systems -- spectral theory -- self-adjoint extensions; 46N50 -- 81Q10; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0013091521000080
• Languages: English
• ISSNs: 0013-0915

Abstract

Abstract: We compute the deficiency spaces of operators of the form $H_A{\hat {\otimes }} I + I{\hat {\otimes }} H_B$, for symmetric $H_A$ and self-adjoint $H_B$ . 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 $H_B$ having discrete, non-degenerate spectrum.