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- W2952752993 abstract "We consider random Schrodinger equations on $bR^d$ or $bZ^d$ for $dge 3$ with uncorrelated, identically distributed random potential. Denote by $lambda$ the coupling constant and $psi_t$ the solution with initial data $psi_0$. Suppose that the space and time variables scale as $xsim lambda^{-2 -kappa/2}, t sim lambda^{-2 -kappa}$ with $0< kappa leq kappa_0$, where $kappa_0$ is a sufficiently small universal constant. We prove that the expectation value of the Wigner distribution of $psi_t$, $bE W_{psi_{t}} (x, v)$, converges weakly to a solution of a heat equation in the space variable $x$ for arbitrary $L^2$ initial data in the weak coupling limit $lambda to 0$. The diffusion coefficient is uniquely determined by the kinetic energy associated to the momentum $v$." @default.
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- W2952752993 date "2005-03-01" @default.
- W2952752993 modified "2023-10-18" @default.
- W2952752993 title "Towards the quantum Brownian motion" @default.
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