Two-particle bound states at interfaces and corners

Roos B, Seiringer R. Two-particle bound states at interfaces and corners. Journal of Functional Analysis. 282(12), 109455.


Journal Article | In Press | English

Scopus indexed
Abstract
We study two interacting quantum particles forming a bound state in d-dimensional free space, and constrain the particles in k directions to (0, ∞)k ×Rd−k, with Neumann boundary conditions. First, we prove that the ground state energy strictly decreases upon going from k to k+1. This shows that the particles stick to the corner where all boundary planes intersect. Second, we show that for all k the resulting Hamiltonian, after removing the free part of the kinetic energy, has only finitely many eigenvalues below the essential spectrum. This paper generalizes the work of Egger, Kerner and Pankrashkin (J. Spectr. Theory 10(4):1413–1444, 2020) to dimensions d > 1.
Keywords
Publishing Year
Date Published
2022-03-09
Journal Title
Journal of Functional Analysis
Acknowledgement
We thank Rupert Frank for contributing Appendix B. Funding from the European Union's Horizon 2020 research and innovation programme under the ERC grant agreement No. 694227 is gratefully acknowledged.
Volume
282
Issue
12
Article Number
109455
ISSN
IST-REx-ID

Cite this

Roos B, Seiringer R. Two-particle bound states at interfaces and corners. Journal of Functional Analysis. 282(12). doi:10.1016/j.jfa.2022.109455
Roos, B., & Seiringer, R. (n.d.). Two-particle bound states at interfaces and corners. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2022.109455
Roos, Barbara, and Robert Seiringer. “Two-Particle Bound States at Interfaces and Corners.” Journal of Functional Analysis. Elsevier, n.d. https://doi.org/10.1016/j.jfa.2022.109455.
B. Roos and R. Seiringer, “Two-particle bound states at interfaces and corners,” Journal of Functional Analysis, vol. 282, no. 12. Elsevier.
Roos B, Seiringer R. Two-particle bound states at interfaces and corners. Journal of Functional Analysis. 282(12), 109455.
Roos, Barbara, and Robert Seiringer. “Two-Particle Bound States at Interfaces and Corners.” Journal of Functional Analysis, vol. 282, no. 12, 109455, Elsevier, doi:10.1016/j.jfa.2022.109455.
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