Non-Cayley-tree model for quasiparticle decay in a quantum dot

The decay of a quasiparticle in a confined geometry, resulting from electro n-electron interactions, has been mapped onto the single-electron problem o f diffusion on a Cayley tree discussed by Altshuler er 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 sa me number of quasiparticles. The model has a recursion relation for the sin gle-particle density of states that is markedly different from that of the Cayley tree. It remains tractable enough such that sufficiently large syste ms con be studied to observe a breakdown of the golden rule of perturbation theory with decreasing excitation energy. [S0031-9007(99)09395-3].