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The Anderson orthogonality exponent K for the overlap of two ground states of a free-electron gas with a local potential at different positions is discussed. In the small-distance limit, it is shown that for arbitrary local potentials K can be expressed in terms of the friction tensor. In the one-dimensional case, K depends on the potential only via the friction coefficient for arbitrary distance, and the exponent is bounded for arbitrary shape of the potential in contrast to the two- or higher-dimensional case. The exact result for K is presented for a short-range potential on a lattice.
K. Schönhammer (Wed,) studied this question.