Abstract:
We consider the weak-coupling limit of the reduced dynamics of an open infinite-dimensional quantum system interacting with an electromagnetic field or a reservoir consisting of Fermi or Bose particles in the dipole approximation. The free Hamiltonian of the system and the system's part of the interaction operator are assumed to be unbounded operators with a continuous spectrum that commute weakly. We find limit values for the multipoint correlation functions of the reservoir and estimate the convergence rate. We then prove that the resulting reduced dynamics of the system converges to unitary dynamics (sometimes called the quantum Cheshire Cat effect) with a modified Hamiltonian, which can be interpreted as a Lamb shift of the original Hamiltonian. We obtain the exact form of the new Hamiltonian and estimate the rate of convergence to the limiting dynamics.
