DNA-seminarium: Quantum transport in a low-density periodic potential: homogenisation via homogeneous flows
- Date: 2/14/2018 at 10:15 AM
- Location: Ångströmlaboratoriet, Lägerhyddsvägen 1
- Lecturer: Jens Marklof (University of Bristol)
- Contact person: Andreas Strömbergsson
Abstract: We show that the time evolution of a quantum particle in a periodic potential converges in a suitable low-density limit, and up second order perturbation theory, to terms that are compatible with the linear Boltzmann equation. This complements results of Eng and Erdos for random potentials, where convergence to the linear Boltzmann equation is proved in all orders. Our analysis suggests, however, that the linear Boltzmann equation fails in the periodic setting for terms of order four and higher. The proofs use Floquet-Bloch theory, multi-variable theta series and equidistribution theorems for homogeneous flows. This is joint work with Jory Griffin (Queens University, Canada).