Jeremy M. Moix, Yang Zhao, Jianshu Cao
An exact method to compute the entire equilibrium reduced density matrix for
systems characterized by a system-bath Hamiltonian is presented. The approach
is based upon a stochastic unraveling of the influence functional that appears
in the imaginary time path integral formalism of quantum statistical mechanics.
This method is then applied to study the effects of thermal noise, static
disorder, and temperature on the coherence length in excitonic systems. As
representative examples of biased and unbiased systems, attention is focused on
the well-characterized light harvesting complexes of FMO and LH2, respectively.
Due to the bias, FMO is completely localized in the site basis at low
temperatures, whereas LH2 is completely delocalized. In the latter, the
presence of static disorder leads to a plateau in the coherence length at low
temperature that becomes increasingly pronounced with increasing strength of
the disorder. The introduction of noise, however, precludes this effect. In
biased systems, it is shown that the environment may increase the coherence
length, but only decrease that of unbiased systems. Finally it is emphasized
that for typical values of the environmental parameters in light harvesting
systems, the system and bath are entangled at equilibrium in the single
excitation manifold. That is, the density matrix cannot be described as a
product state as is often assumed, even at room temperature. The reduced
density matrix of LH2 is shown to be in precise agreement with the steady state
limit of previous exact quantum dynamics calculations.
View original:
http://arxiv.org/abs/1202.4705
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