• The Journal of the Korea institute of electronic communication sciences
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• v.7 no.4
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• pp.855-859
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• 2012

This study derives a generalized PSD formula in the LTV phase noise theory for noisy oscillators. The derived formula analytically proves that the LTV phase noise theory can predict the conservation of the power in the noisy oscillation signals. Additionally, the derived formula allows the theory to account for the behavior of the power spectrum over the entire frequency range including the regions around higher harmonics as well as fundamental frequency.

• Bulletin of the Korean Chemical Society
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• v.35 no.3
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• pp.858-864
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• 2014

Recently, many researches have shown that even photosynthetic light-harvesting pigment-protein complexes can have quantum coherence in their excitonic energy transfer at cryogenic and physiological temperatures. Because the protein supplies such noisy environment around pigments that conventional wisdom expects very short lived quantum coherence, elucidating the mechanism and searching for an applicability of the coherence have become an interesting topic in both experiment and theory. We have previously studied the quantum coherence of a phycocyanin 645 complex in a marine algae harvesting light system, using Poisson mapping bracket equation (PBME). PBME is one of the applicable methods for solving quantum-classical Liouville equation, for following the dynamics of such pigment-protein complexes. However, it may suffer from many defects mostly from mapping quantum degrees of freedom into classical ones. To make improvements against such defects, benchmarking targets with more accurately described dynamics is highly needed. Here, we fall back to reduced hierarchical equation of motion (HEOM), for such a purpose. Even though HEOM is known to applicable only to simplified system that is coupled to a set of harmonic oscillators, it can provide ultimate accuracy within the regime of quantum-classical description, thus providing perfect benchmark targets for certain systems. We compare the evolution of the density matrix of pigment excited states by HEOM against the PBME results at physiological temperature, and observe more sophisticated changes of density matrix elements from HEOM. In PBME, the population of states with intermediate energies display only monotonically increasing behaviors. Most importantly, PBME suffers a serious issue of wrong population in the long time limit, likely generated by the zero-point energy leaking problem. Future prospects for developments are briefly discussed as a concluding remark.