TY - JOUR
T1 - Effective dynamics for Bloch electrons: Peierls substitution and beyond
Y1 - 2003
A1 - Gianluca Panati
A1 - Herbert Spohn
A1 - Stefan Teufel
AB - 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.
PB - Springer
UR - http://hdl.handle.net/1963/3040
U1 - 1293
U2 - Mathematics
U3 - Mathematical Physics
ER -