%0 Journal Article
%D 2003
%T Effective dynamics for Bloch electrons: Peierls substitution and beyond
%A Gianluca Panati
%A Herbert Spohn
%A Stefan Teufel
%X We consider an electron moving in a periodic potential and subject to an additional slowly varying external electrostatic potential, $\\\\phi(\\\\epsi x)$, and vector potential $A(\\\\epsi x)$, with $x \\\\in \\\\R^d$ and $\\\\epsi \\\\ll 1$. We prove that associated to an isolated family of Bloch bands there exists an almost invariant subspace of $L^2(\\\\R^d)$ and an effective Hamiltonian governing the evolution inside this subspace to all orders in $\\\\epsi$. To leading order the effective Hamiltonian is given through the Peierls substitution. We explicitly compute the first order correction. From a semiclassical analysis of this effective quantum Hamiltonian we establish the first order correction to the standard semiclassical model of solid state physics.
%I Springer
%G en_US
%U http://hdl.handle.net/1963/3040
%1 1293
%2 Mathematics
%3 Mathematical Physics
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