Decoherence harmonic bath

Decoherence is usually modeled by coupling the system to a large reservoir of, e.g., harmonic oscillators. Here two different types of couplings need to be distinguished which are indicated in Fig. 3. These are collective interactions, Fig. 3 (a), where all particles couple to the same bath and individual interactions, Fig. 3 (b), where each particle couples to its own, independent reservoir. In the third contribution by C. Mewes et al. only the second type of coupling is considered. It is well suited for the case of a dilute atomic vapor. 

The stochastic mean-field [20] (SMF) method simultaneously resolves the following two major issues with NA MD. First, decoherence effects within the quantum subsystem that take place due to its interaction with an environment are included. Second, decoherence naturally leads to the asymptotic branching of NA trajectories. That is, the implementation of the decoherence effect in the SMF approach automatically resolves the branching problem. By extending the ordinary quantum-classical MF approximation, the SMF approach accounts for the quantum features of the environment in the Lindblad formulation. The Lindblad formulation is exact for a bath of harmonic oscillators and is an approximation for other types of solvents. While the quantum nature of the environment is treated by SMF within an approximation, its classical properties are included exactly by classical MD with a true Hamiltonian. 

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