Effective Quantum Dynamics of Interacting Systems with Inhomogeneous   Coupling
  We study the quantum dynamics of a single mode/particle interacting inhomogeneously with a large number of particles and introduce an effective approach to find the accessible Hilbert space where the dynamics takes place. Two relevant examples are given: the inhomogeneous Tavis-Cummings model (e.g., N atomic qubits coupled to a single cavity mode, or to a motional mode in trapped ions) and the inhomogeneous coupling of an electron spin to N nuclear spins in a quantum dot. 
C.E. Lopez, H. Christ, J.C. Retamal, and E. Solano