  Spin-dependent charge transfer decay in an alkali atom doped polyacetylene is
studied in terms of the complex spectral analysis, revealing the single-spin
Zeeman splitting influenced by the spin-orbit interaction. Nonhermitian
effective Hamiltonian has been derived from the total system hermitian
Hamiltonian using Brillouin-Wigner-Feshbach projection method, where the
microscopic spin-dependent dissipation effect is correctly incorporated in the
energy-dependent self-energy. Since the present method maintains the dynamical
and chiral symmetries of the total system, we discovered two types of
exceptional point (EP) singularities in a unified perspective: the EP surface
and EP ring are attributed to the dynamical and chiral symmetry breaking,
respectively. We have revealed that the coherent single-spin electron resonance
(SSESR) spectrum reflects the complex eigenenergy spectrum of the system. We
have formulated the SSESR spectrum in terms of the nonlinear response function
in the Liouville-space pathway approach, where we have constructed the
Liouville space basis using the complex eigenstates of the total Hamiltonian.
We have calculated the one- and two-dimensional Fourier transform SSESR (1DFT
and 2DFT) spectra reflecting the spin-relaxation dynamics at the donor site.
While the 1DFT SSESR spectrum reflects the complex eigenenergy spectrum, the
2DFT gives detailed information on the quantum coherence in the spin-relaxation
dynamics as a cross-correlation between the two frequencies. We found a giant
response of the coherent SSESR around the EP ring singularity due to the
vanishing normalization factors at the EP ring and the resonance effect. We
have discovered that the giant response is much larger in magnitudes in the
2DFT spectrum than in the 1DFT spectrum, which promises the 2DFT SSESR a useful
tool to observe the single-spin response in a molecule.
