Propagator connection with density matrix

In order to connect Eqs. 17.14-17.15 with classical molecular dynamics on the fly the diagonal density matrix elements pu q, p, t) which are functions of the coordinates q and momenta p can be represented by independent trajectories propagated in the ground and excited electronic states, respectively. Thus, employing a number of Ntraj trajectories, puiq,p,t) can be represented by a swarm of time-dependent 5 functions... 

This effect may also cause an oscillatory instability of the front propagation in the case of the isothermal mechanism of the auto wave process. However, in this case a jumplike onset of dispersion in the next layer of the solid matrix will be connected not with the critical temperature gradient of thermal fracture, but with the critical concentration of the final product accumulated at the boundary of this layer (fracture due to a local alteration of the density). 

---