Keywordssecond-order differential equations; optical pumping; analytical solutions; 02.30.Hq; 32.80.Xx; 32.30.-r; recurrence relations; harmonic chain; local dynamics; ergodicity; chaos; Hamiltonian mechanics; coupled oscillators; Lorentz transformation; Dirac equation; 45.20.Jj; 47.10.Df; 41.75; 41.85; 03.65.Pm; 05.45.Xt; 03.30.+p; 03.65.-w; 29.27.-a; nonlinear coherent states; nonclassicality; squeezed states; entanglement entropy; generalized harmonic oscillator; paraxial wave equation; nonlinear schrödinger-type equations; riccati systems; solitons; J0101; inverted harmonic oscillator; harmonic trap; Kepler-Coulomb problem; Kustaanheimo-Stiefel transformation; Gaussian entanglement; two coupled harmonic oscillators; coupled Lorentz groups; space-time separation; Wigner’s little groups; O(3, 2) group; Dirac’s generators for two coupled oscillators; 2D semimetals; Dirac–Hartree–Fock self-consistent field approximation; Majorana-like field; Weyl-like nodes; Fermi velocity operator
