Unitary unfoldings of Bose-Hubbard exceptional point with and without particle number conservation
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866917105587191808 |
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| author | Znojil, Miloslav |
| author_facet | Znojil, Miloslav |
| contents | Non-Hermitian but ${\cal PT}-$symmetric quantum system of an $N-$plet of bosons described by the three-parametric Bose-Hubbard Hamiltonian $H(γ,v,c)$ is picked up, in its special exceptional-point limit $c \to 0$ and $γ\to v$, as an unperturbed part of the family of generalized Bose-Hubbard-like Hamiltonians $\mathfrak{H}(λ)=H(v,v,0)+λ\,{\cal V}$ for which the unitarity of the perturbed system is required. This leads to the construction of two different families of Hamiltonians $\mathfrak{H}(λ)$. In the first one the number $N$ of bosons is assumed conserved while in the second family such an assumption is relaxed. In both cases the anisotropy of the related physical Hilbert space is shown reflected by a highly counterintuitive but operationally realizable structure of admissible perturbations $λ\,{\cal V}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_12844 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Unitary unfoldings of Bose-Hubbard exceptional point with and without particle number conservation Znojil, Miloslav Mathematical Physics High Energy Physics - Theory Quantum Physics Non-Hermitian but ${\cal PT}-$symmetric quantum system of an $N-$plet of bosons described by the three-parametric Bose-Hubbard Hamiltonian $H(γ,v,c)$ is picked up, in its special exceptional-point limit $c \to 0$ and $γ\to v$, as an unperturbed part of the family of generalized Bose-Hubbard-like Hamiltonians $\mathfrak{H}(λ)=H(v,v,0)+λ\,{\cal V}$ for which the unitarity of the perturbed system is required. This leads to the construction of two different families of Hamiltonians $\mathfrak{H}(λ)$. In the first one the number $N$ of bosons is assumed conserved while in the second family such an assumption is relaxed. In both cases the anisotropy of the related physical Hilbert space is shown reflected by a highly counterintuitive but operationally realizable structure of admissible perturbations $λ\,{\cal V}$. |
| title | Unitary unfoldings of Bose-Hubbard exceptional point with and without particle number conservation |
| topic | Mathematical Physics High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2008.12844 |