Stochastic Dynamics on the Level of Pure States

We have argued heuristically that certain molecular states are unstable under external perturbations. The symmetric ground state 4 + of an ammonia-type molecule, for example, seems to be unstable under external 

The pure state of the molecular environment is never precisely known. Since the dynamics of the molecular pure state depends on this unknown environment s (pure) state, one gets a stochastic dynamics for the molecular pure states. For a two-level system-with its pure states describable by a Bloch sphere—the situation is illustrated in Fig. 8. The dynamics of some given molecular initial state is governed not only by the Schrodinger equation, but also by external influence. Depending on the (pure) state of the environment, we reach different final molecular states. Usually only probabilistic predictions can be given (and no information about the precise trajectory of pure states, i.e., the trajectory on the Bloch sphere). 

Stochastic dynamics for the pure states of a quantum system have been proposed or derived in a variety of different contexts. Also, the transition rates of Fermi s golden rule,  

Unfortunately, a rigorous derivation of stochastic pure-state dynamics is still lacking. Nevertheless it is gratifying that such stochastic dynamics are important and in fact form the basis of a quantum theory of individual (quantum) objects. One hint in this direction comes from single-molecule spectroscopy (SMS), where single molecule always is to be understood as a single molecule embedded into a polymorphic matrix or a crystal.The example used in Fig. 9 is a single 

FIGURE 8 Sketch of a stochastic dynamics for pure states of a two-level molecule Starting from an arbitrary initial state, one ends up with certain states such as, for example, eigenstates of some operator. Which final state is reached depends on the (pure) state of the molecular environment. 

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