Work

Zernike system revisited: Imaginary gauge and Higgs oscillator

Year: 2025

Type: article

Abstract: We analyze the recently proposed classical/quantum mechanical interpretation of Zernike system and establish its equivalence to the Higgs oscillator on sphere or pseudosphere (Lobachevsky plane). We show that the non-reality of the classical Zernike Hamiltonian is an insignificant artifact of imaginary gauge and can be eliminated with a canonical transformation. The quantum counterpart of this canonical transformation is a similarity transformation mapping the system to the quantum Higgs oscillator with integration measure depending on [Formula: see text] parameters. When [Formula: see text], it results in the Hermitian Hamiltonian describing a free particle on (pseudo)sphere, while deviation from this point leads to a pseudo-Hermitian system.

Source: Modern Physics Letters A

DOI: 10.1142/s0217732325502220

Authors: Vahagn Abgaryan, Armen Nersessian, Vahagn Yeghikyan

Institutions: A. Alikhanyan National Laboratory, Joint Institute for Nuclear Research, Institute of Radiophysics and Electronics

Language: English

Topic: Quantum Mechanics and Non-Hermitian Physics

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funder: State Committee of Science

Awards: G5900365043, G5987077161