论文标题
Bose-Hubbard的统一特殊点有和没有粒子数量保存
Unitary unfoldings of Bose-Hubbard exceptional point with and without particle number conservation
论文作者
论文摘要
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} $，需要扰动系统的单位性。这导致建立了两个不同家庭的汉密尔顿家族$ \ mathfrak {h}（λ）$。在第一个中，假设在第二个家庭中，假设玻色子的数字$ n $是保守的。在这两种情况下，相关物理希尔伯特空间的各向异性都通过高度违反直觉但可接收的扰动的可实现结构$λ\，{\ cal V} $反映。
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 $λ\,{\cal V}$.
