Long-Range Energy-Level Interaction in Small Metallic Particles

Details Long-Range Energy-Level Interaction in Small Metallic Particles Long-Range Energy-Level Interaction in Small Metallic Particles

1993-02-19

arxiv.org/abs/cond-mat/9302029v1

Europhys.Lett.24:1,1993

Physics

Condensed Matter

Saclay-s93/014 Email: pichard@amoco.saclay.cea.fr

Scientific paper

10.1209/0295-5075/24/1/001

We consider the energy level statistics of non-interacting electrons which diffuse in a $ d $-dimensional disordered metallic conductor of characteristic Thouless energy $ E_c. $ We assume that the level distribution can be written as the Gibbs distribution of a classical one-dimensional gas of fictitious particles with a pairwise additive interaction potential $ f(\varepsilon ). $ We show that the interaction which is consistent with the known correlation function of pairs of energy levels is a logarithmic repulsion for level separations $ \varepsilon E_c, $ $ f(\varepsilon ) $ vanishes as a power law in $ \varepsilon /E_c $ with exponents $ -{1 \over 2},-2, $ and $ -{3 \over 2} $ for $ d=1,2, $ and 3, respectively. While for $ d=1,2 $ the energy-level interaction is always repulsive, in three dimensions there is long-range level attraction after the short-range logarithmic repulsion. Email contact: pichard@amoco.saclay.cea.fr

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