Non-Cayley-Tree Model for Quasiparticle Decay in a Quantum Dot

The decay of a quasiparticle in a confined geometry, resulting from electron-electron interactions, has been mapped onto the single-electron problem of diffusion on a Cayley tree discussed by Altshuler et al. [Phys. Rev. Lett. 78, 2803 (1997)]. We study an alternative model that captures the strong correlations between the self-energies of different excitations with the same number of quasiparticles. The model has a recursion relation for the single-particle density of states that is markedly different from that of the Cayley tree. It remains tractable enough such that sufficiently large systems can be studied to observe a breakdown of the golden rule of perturbation theory with decreasing excitation energy.