A remark on charge transfer processes in multi-particle systems

Details A remark on charge transfer processes in multi-particle systems A remark on charge transfer processes in multi-particle systems

2010-05-19

arxiv.org/abs/1005.3387v3

Physics

Mathematical Physics

Scientific paper

We assess the probability of resonances between sufficiently distant states $\ux=(x_1, ..., x_N)$ and $\uy=(y_1, ..., y_N)$ in the configuration space of an $N$-particle disordered quantum system. This includes the cases where the transition $\ux \rightsquigarrow \uy$ "shuffles" the particles in $\ux$, like the transition $(a,a,b) \rightsquigarrow (a, b, b)$ in a 3-particle system. In presence of a random external potential $V(\cdot, \omega)$ (Anderson-type models) such pairs of configurations $(\ux,\uy)$ give rise to local (random) Hamiltonians which are strongly coupled, so that eigenvalue (or eigenfunction) correlator bounds are difficult to obtain (cf. \cite{AW09a}, \cite{CS09b}). This difficulty, which occurs for $N\ge 3$, results in eigenfunction decay bounds weaker than expected. We show that more efficient bounds, obtained so far only for 2-particle systems \cite{CS09b}, extend to any $N>2$.

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