The minimally anisotropic metric operator in quasi-Hermitian quantum mechanics

0494793 - ÚJF 2019 RIV GB eng J - Článek v odborném periodiku
Krejčiřík, D. - Lotoreichik, Vladimir - Znojil, Miloslav
The minimally anisotropic metric operator in quasi-Hermitian quantum mechanics.
Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences. Roč. 474, č. 2217 (2018), č. článku 20180264. ISSN 1364-5021. E-ISSN 1471-2946
Grant CEP: GA ČR GA17-01706S; GA ČR GA16-22945S
Institucionální podpora: RVO:61389005
Klíčová slova: quasi-Hermitian quantum mechanics * metric operator * similarity transforms * PT-symmetry * basis properties
Obor OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impakt faktor: 2.818, rok: 2018

We propose a unique way to choose a new inner product in a Hilbert space with respect to which an originally non-self-adjoint operator similar to a self-adjoint operator becomes self-adjoint. Our construction is based on minimizing a 'Hilbert-Schmidt distance' to the original inner product among the entire class of admissible inner products. We prove that either the minimizer exists and is unique or it does not exist at all. In the former case, we derive a system of Euler-Lagrange equations by which the optimal inner product is determined. A sufficient condition for the existence of the unique minimally anisotropic metric is obtained. The abstract results are supported by examples in which the optimal inner product does not coincide with the most popular choice fixed through a charge-like symmetry.
Trvalý link: http://hdl.handle.net/11104/0287853