Dissipation in anharmonic molecular systems: beyond the linear coupling limit Original Research Article

Open-system density matrix theory is a powerful method for treating the dynamics of an active quantum mechanical system embedded in a “bath” of less active modes. For the sake of economy and conceptual simplicity, the system and bath modes are often considered harmonic and the coupling between them bilinear in the system and bath coordinates. We present a systematic way of how to include nonlinear position dependence of the coupling strength between an anharmonic system and a bath. This extends the applicability of open-system density matrix theory considerably, while still retaining the advantages of the harmonic-linear model. To achieve this we suggest to interpret operators derived from supersymmetric quantum mechanics as approximate raising/lowering operators, and to use them for constructing a dissipative Liouvillian of Lindblad form. The properties of this Liouvillian are examined in some detail. As a concrete example, we apply the formalism to the vibrational relaxation and the inelastic scattering of a gas phase atom (argon) at a surface. The method will also be generalized to finite temperatures.