Quantum reaction rates and sampling of quantum equilibrium structure.

Quantum time correlation functions obtained from the linear response theory are defined in terms of a scalar product involving the Kubo transform. This form of the scalar product also insures that the nonequilibrium average of the random force fluctuations corresponding to an observable vanish so that the macroscopic law is obtained on long distance and time scales and the Onsager regression hypothesis is satisfied. For example, consider a reaction A B where species A and B are defined microscopically by operators N̂A,B, respectively. The time dependent quantum forward reaction rate is given by the Kubo-transformed reactive flux correlation function, k t nA =− N̂ A ; N̂B t , where nA eq is the equilibrium density of species A. The rate constant is given by k=limt→ k t . Introducing Wigner transforms, we can write an alternative but equivalent form of k t as