Dependence of the steady state of a nonlinear degenerate molecular dimer on the character of dissipative coupling

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Abstract
The dynamics of quasiparticle transport in a degenerate adiabatic molecular dimer with dissipative as well as nonlinear local site coupling has been analyzed. The dissipative part of the model is based on the Haken-Strobl type of Liouville equation for a density matrix that includes multichannel coupling to a dissipative environment and, moreover, the additional nonlinear term of polaronic type. The theory of positive semigroups has been applied in deriving equations of motion for components of the Bloch vector that satisfy requirements of a relaxing semigroup. The presence of only one decay channel, represented by local dissipative coupling, always leads to the long-time equalization of site-occupation probabilities. We have shown that whether the nonsymmetrical steady state is reached or not depends exclusively on the properties of the Haken-Strobl dissipative part of Liouvillian, regardless of the nonlinear coupling. Clearly, the magnitude of the asymmetry, if it occurs, is influenced by the strength of the nonlinear local site coupling.