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Nonequilibrium Transport of Quantum Molecular Chain in terms of the Complex Liouvillian Spectrum

Transport process in molecular chain in nonequilibrium stationary state is theoretically investigated. The molecule is interacting at its both ends with thermal baths which has different temperatures, while no dissipation mechanism is contained inside the molecular chain. We have first obtained the nonequilibrium stationary state outside the Hilbert space in terms of the complex spectral representation of Liouvillian. The nonequilibrium stationary state is obtained as an eigenstate of the Liouvillian which is constructed through the collision invariant of the kinetic equation. The eigenstate of the Liouvillian contains an information of spatial correlation between the molecular chain and the thermal baths. While energy flow in the nonequilibrium state which is due to the first order correlation can be described by Landauer formula, the particle current due to the second order correlation cannot be described by the Landauer formula. The present method provides a simple and perspective way to evaluate the energy transport of molecular chain under the nonequilibrium situation.