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A remark on charge transfer processes in multi-particle systems

We assess the probability of resonances between sufficiently distant states in a combinatorial graph serving as the configuration space of an N-particle disordered quantum system. This includes the cases where the transition "shuffles" the particles in the configurations. In presence of a random external potential V, such pairs of configurations give rise to local (random) Hamiltonians which are strongly coupled, so that eigenvalue (or eigenfunction) correlator bounds are difficult to obtain. This difficulty, which occurs for three or more particles, results in eigenfunction decay bounds weaker than expected. We show that more efficient bounds, obtained so far only for 2-particle systems, extend to any number of particles.