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• W2953022194 abstract "We consider random Schrodinger equations on $bZ^d$ for $dge 3$ with identically distributed random potential. Denote by $lambda$ the coupling constant and $psi_t$ the solution with initial data $psi_0$. The space and time variables scale as $xsim lambda^{-2 -kappa/2}, t sim lambda^{-2 -kappa}$ with $0< kappa < kappa_0(d)$. We prove that, in the limit $lambda to 0$, the expectation of the Wigner distribution of $psi_t$ converges weakly to a solution of a heat equation in the space variable $x$ for arbitrary $L^2$ initial data. The diffusion coefficient is uniquely determined by the kinetic energy associated to the momentum $v$. This work is an extension to the lattice case of our previous result in the continuum cite{ESYI}, cite{ESYII}. Due to the non-convexity of the level surfaces of the dispersion relation, the estimates of several Feynman graphs are more involved." @default.
• W2953022194 created "2019-06-27" @default.
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• W2953022194 date "2005-02-07" @default.
• W2953022194 modified "2023-10-18" @default.
• W2953022194 title "Quantum diffusion for the Anderson model in the scaling limit" @default.
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