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

0534289 - ÚJF 2021 RIV GB eng J - Článek v odborném periodiku
Znojil, Miloslav
Unitary unfoldings of a Bose-Hubbard exceptional point with and without particle number conservation.
Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences. Roč. 476, č. 2242 (2020), č. článku 20200292. ISSN 1364-5021. E-ISSN 1471-2946
Institucionální podpora: RVO:61389005
Klíčová slova: quantum mechanics * quasi-Hermitian observables * dynamics near exceptional points * Bose-Hubbard Hamiltonians * stability-guaranteeing perturbations
Obor OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impakt faktor: 2.704, rok: 2020
Způsob publikování: Omezený přístup
https://doi.org/10.1098/rspa.2020.0292

The conventional non-Hermitian but PT-symmetric three-parametric Bose-Hubbard Hamiltonian H(gamma, v, c) represents a quantum system of N bosons, unitary only for parameters gamma, v and c in a domain D. Its boundary partial derivative D contains an exceptional point of order K (EPK, K=N+1) at c=0 and gamma=v, but even at the smallest non-vanishing parameter c not equal 0 the spectrum of H(v, v, c) ceases to be real, i.e. the system ceases to be observable. In this paper, the question is inverted: all of the stable, unitary and observable Bose-Hubbard quantum systems are sought which would lie close to the phenomenologically most interesting EPK-related dynamical regime. Two different families of such systems are found. Both of them are characterized by the perturbed Hamiltonians H(lambda)=H(v,v,0)+lambda V for which the unitarity and stability of the system is guaranteed. In the first family the number N of bosons is assumed conserved while in the second family such an assumption is relaxed. Attention is paid mainly to an anisotropy of the physical Hilbert space near the EPK extreme. We show that it is reflected by a specific, operationally realizable structure of perturbations lambda V which can be considered small.
Trvalý link: http://hdl.handle.net/11104/0312514