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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 $A(\epsi x)$…
Effective N-body dynamics for the massless Nelson model and adiabatic decoupling without spectral gap
Stefan Teufel
The Schroedinger equation for N particles interacting through effective pair potentials is derived from the massless Nelson model with ultraviolet cutoffs. We consider a scaling li…
Space-adiabatic Decoupling to All Orders
Gianluca Panati, Herbert Spohn, Stefan Teufel
A systematic perturbation scheme is developed for approximate solutions to the time-dependent Schroedinger equation with a space-adiabatic Hamiltonian. For a particular isolated en…
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…