In the first part of this lecture, I will discuss the proof of convergence of the Lorentz process, in the Boltzmann-Grad limit, to a random process governed by a generalised linear Boltzmann equation. This will hold for general scatterer configurations, including certain types of quasicrystals, and include the previously known cases of periodic and Poisson random scatterer configurations. The second part of the lecture will focus on quantum transport in the periodic Lorentz gas in a combined short-wavelength/Boltzmann-Grad limit, and I will report on some partial progress in this challenging problem. Based on joint work with Andreas Strombergsson (part I) and Jory Griffin (part II).
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- Partial Differential Equations Seminar