Level Statistics and Localization for Two Interacting Particles in a Random Potential

Abstract

We consider two particles with a local interaction $U$ in a random potential at a scale $L_1$ (the one particle localization length). A simplified description is provided by a Gaussian matrix ensemble with a preferential basis. We define the symmetry breaking parameter $\mu \propto U^{-2}$ associated to the statistical invariance under change of basis. We show that the Wigner-Dyson rigidity of the energy levels is maintained up to an energy $E_{\mu }$. We find that $E_{\mu }\propto 1/\sqrt{\mu }$ when $\Gamma$ (the inverse lifetime of the states of the preferential basis) is smaller than ${\Delta }_2$ (the level spacing), and $E_{\mu }\propto 1/\mu$ when $\Gamma >{\Delta }_2$. This implies that the two-particle localization length $L_2$ first increases as $|U|$ before eventually behaving as $U^2$.

4 pages REVTEX, 4 Figures EPS, UUENCODED

References in corpus (1)

• Effective $\sigma$ Model Formulation for Two Interacting Electrons in a Disordered Metal

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