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Equation s6d is derived assuming kBl=0, which is exact in the linear coupling limit, Eq. s5d. In the strong coupling case discussed below, kBl ≠ 0 leads to an additional coherent transfer route which is, however, strongly damped and may be disregarded; see, e.g., D. Segal and A. Nitzan, Chem. Phys. 281, 235 (2002)
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Note that the result Eq. s15d holds only for small GKsK=L,Rd because the broadening of the oscillator frequency was not taken into account. The result of the full quantum treatment of Ref. 30 Tsvd=s2/ pd v2GLGRfsv2 - v0 2d2+sGL+GRd2v2g-1 remains finite in the limit GK!. For the analogous consideration in the electron conduction case see Ref. 44.
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51
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21444442081
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note
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It can be easily verified that the same result is obtained from the expression for the heat flux out of the left bath.
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