2020/08/28 by Znojil, Miloslav
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2008.12844
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 → 0 and γ→ v, as an unperturbed part of the family of generalized Bose-Hubbard-like Hamiltonians \mathfrakH(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 \mathfrakH(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.