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The Kronig-Penney model with arbitrary scattering potentials theories

Thomas BUSCH (Okinawa Institute for Science and Technology, Okinawa, Japan)
When Aug 22, 2019
from 01:30 PM to 02:30 PM
Where Salle Est/Ouest du M7
Attendees Thomas BUSCH
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Jeudi 22 Août

 

Title:  The Kronig-Penney model with arbitrary scattering potentials

Thomas BUSCH (Okinawa Institute for Science and Technology, Okinawa, Japan)

 

Abstract:  

Motivated by the recent realisation of a Kronig-Penney lattice for ultra cold atoms, I will discuss exact solutions to such a system with arbitrary positions and strengths of scattering sites. This is an iconic model in solid state physics and the large number of degrees of freedom that come from the possibility to arbitrarily choose the properties of the scatterers allow to explore a wide range of physics.
 
As an example I will show that this one-dimensional model can possess topologically nontrivial properties. Using some of the free parameters of the system as extra dimensions allows to observe topologically protected edge states as well as the emergence of a Hofstadter butterfly-like quasimomentum spectrum, even in the case of small numbers of scattering sites. To extend these results to strongly interacting many-particle systems I will also briefly discuss the solutions in the Tonks-Girardeau limit.