The dynamics of 1D Bloch electrons in constant electric fields
F. Bentosela, P. Duclos, G. Nenciu, V. Moldoveanu
Abstract
We study the dynamics of a 1D Bloch electron subjected to a constant electric field. The periodic potential is supposed to be less singular than the δ-like potential (Dirac comb). We give a rigorous proof of Ao's result Ao that for a large class of initial conditions (high momentum regime) there is no localization in momentum space. The proof is based on the mathematical substantiation of the two simplifying assumptions made in physical literature: the transitions between far away bands can be neglected and the transitions at the quasi-crossing can be described by Landau-Zener like formulae. Using the connection between the above model and the driven quantum ring (DQR) shown by Avron and Nemirovski AvN, our results imply the increase of energy for weakly singular such DQR and appropiate initial conditions.
Create a lesson
Related papers
On the Geometric Structure of Hyperbolic Clifford Bundles and Associated Spin Groups
Eduardo Notte-Cuello
Koopman-von Neumann formalism meets contact Hamiltonian systems
Federico Zadra
Lossless propagation bounds for long-range fermionic interactions
Stefan Teufel
Supersymmetric Neuromorphic FitzHugh--Nagumo model
D. Maroulakos, A. Wal, S. K. Mishra et al.
Separatrix splitting in a multiferroic neuromorphic oscillator: toward Arnold diffusion
D. Maroulakos, Z. Toklikishvili, A. Wal et al.
Anderson localisation in infinite and finite resonator crystals with long-range interactions
Habib Ammari, Xin Fu, Wenjia Jing et al.