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Effective dynamics for Bloch electrons: Peierls substitution and beyond
Gianluca Panati, Herbert Spohn, Stefan Teufel
We consider an electron moving in a periodic potential and subject to an additional slowly varying external electrostatic potential, $ϕ(\epsi x)$, and vector potential $A(\epsi x)$…
Last Branching in Directed Last Passage Percolation
Patrik L. Ferrari, Herbert Spohn
The 1+1 dimensional directed polymers in a Poissonean random environment is studied. For two polymers of maximal length with the same origin and distinct end points we establish th…
Ground state degeneracy of the Pauli-Fierz Hamiltonian inlcuding spin
F. Hiroshima, H. Spohn
We consider an electron, spin 1/2, minimally coupled to the quantized radiation field in the nonrelativistic approximation, a situation defined by the Pauli-Fierz Hamiltonian .…
Space-Adiabatic Perturbation Theory
Gianluca Panati, Herbert Spohn, Stefan Teufel
We study approximate solutions to the Schrödinger equation $i\epsi\partialψ_t(x)/\partial t = H(x,-i\epsi\nabla_x) ψ_t(x)$ with the Hamiltonian given as the Weyl quantization of th…