INTERACTION BETWEEN 2-LEVEL SYSTEMS IN METALS

We consider two particles placed in the sea of metallic electrons. One particle is assumed to be jumping between two sites, the other also between two other sites. We calculate the energy of this system by perturbation expansion in terms of the particle-electron interaction. In the fourth order, we find a term proportional to log T, which depends on the relative position vectors of the four sites. Surprisingly, this term does not tend to zero, even when the tunneling matrices for the jumping particles tend to zero. When the tunneling matrices are exactly zero, the particles are fixed to one of the sites and the energy does not involve such a singular term.