The stability of the hydrogen molecule interacting with the environment according to the balanced gain and loss energy scheme was studied. We determined the properties of the molecule taking into account all electronic interactions, the parameters of the Hamiltonian being computed by the variational method. The interaction of the hydrogen molecule with the environment was modeled parametrically (γ) by means of the non-Hermitian, P T -symmetric Hamiltonian. We showed that the hydrogen molecule is dynamically unstable. Its dissociation time (TD) decreases if the γ parameter increases (for γ → 0 we got TD → + ∞). The dynamic instability of the hydrogen molecule is superimposed on the decrease in its static stability as γ increases. Then we can observe the decrease in the dissociation energy value and the existence of the metastable state of the molecule as γMS reaches 0.659374 Ry. The hydrogen molecule is statically unstable when γ > γD = 1.024638 Ry. Moreover, we can also observe the P T symmetry breaking effect for the electronic Hamiltonian when γ P T = 0.520873 Ry. This effect does not affect such properties of the hydrogen molecule as: the electronic Hamiltonian parameters, the phonon and the rotational energies, and the values of the electron-phonon coupling constants neither it disturbs the dynamics of the electronic subsystem. However, the number of available quantum states goes down to four.

Institute of Physics Jan Długosz University Ave Armii Krajowej 19 42 200 Czȩstochowa Poland

Institute of Physics Jan Długosz University in Czȩstochowa Ave Armii Krajowej 13 15 42 200 Czȩstochowa Poland

Joint Laboratory of Optics of Palacký University and Institute of Physics of CAS RCPTM Faculty of Science Palacký University 17 listopadu 12 771 46 Olomouc Czech Republic

Quantum Optics and Engineering Division Faculty of Physics and Astronomy University of Zielona Góra Prof Z Szafrana 4a 65 516 Zielona Góra Poland

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Sci Rep. 2020 Mar 19;10(1):5084. doi: 10.1038/s41598-020-61865-8. PubMed

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