Unitary unfoldings of Bose-Hubbard exceptional point with and without particle number conservation

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Auteur principal: Znojil, Miloslav
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Publié: 2020
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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