Publisher Correction: Interaction of the hydrogen molecule with the environment: stability of the system and the [Formula: see text] symmetry breaking.

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Interaction of the hydrogen molecule with the environment: stability of the system and the [Formula: see text] symmetry breaking.

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, [Formula: see text]-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 [Formula: see text] symmetry breaking effect for the electronic Hamiltonian when [Formula: see text] = 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.

Influence of external extrusion on stability of hydrogen molecule and its chaotic behavior.

We have determined the stability conditions of the hydrogen molecule under the influence of an external force of harmonic-type explicitly dependent on the amplitude (A) and frequency (Ω). The ground state of the molecule has been determined in the framework of the Born-Oppenheimer approximation, whereas the energy of the electronic subsystem has been calculated using the Hubbard model including all two-site electron interactions. The diagram of RT0 (A,Ω), where RT0 denotes the distance between protons after the fixed initial time T0, allowed us to visualize the area of the instability with the complicated structure. We have shown that the vibrations of the hydrogen molecule have a chaotic nature for some points of the instability region. In addition to the amplitude and frequency of the extrusion, the control parameter of the stability of the molecule is the external force associated with pressure. The increase in its value causes the disappearance of the area of the instability and chaotic vibrations.

Partial potentials of selected cardiac muscle regions and heart activity model based on single fibres.

We present single fibre heart activity model (SFHAM) based on the current flow through the five bunches of fibres of the cardiac muscle (CM). The five effective fibres are identified and assigned to the appropriate segments of CM. Analytical functions describing ionic flows along the fibres are derived and proposed. The parameters determining the shapes and amplitudes of the functions proposed are obtained on the basis of standard 12-lead ECG measurements after numerical fitting procedures concentrating on the QRS-waves. As a consequence, five independent courses of partial, transient potentials are obtained representing: anterior, inferior, lateral, posterior walls, and interventricular septum activities, respectively. Moreover, to check our theoretical results we compare the potentials calculated with those from physical measurements performed on the patient's body surface. We expect that SFHAM will permit detection of pathological changes in particular fragments of CM.

Wigner-function nonclassicality as indicator of quantum chaos.

We propose a Wigner-function-based parameter that can be used as an indicator of quantum chaos. This parameter is defined as "entropy" from the time dependence of "nonclassicality" proposed by A. Kenfack and K. Zyczkowski [J. Opt. B 6, 394 (2004)]. We perform our considerations for the system of damped nonlinear (Kerr-like) oscillator excited by a series of ultrashort external pulses.