Mark Kac Seminar

December 12, 2008






Location: Utrecht, KNG80, room 130


speaker: Evgeny Verbitskiy (Philips Research / RU Groningen)

title: Abelian Sandpiles and the Harmonic Model



We present a construction of an entropy-preserving equivariant surjective map from the d-dimensional critical sandpile model to a certain compact abelian group (the `harmonic model'). A similar map is constructed for the dissipative abelian sandpile model and is used to prove uniqueness and the Bernoulli property of the measure of maximal entropy for that model.

The talk is based on a joint work with Klaus Schmidt (Vienna).



speaker: Wojciech De Roeck (ETH Zürich)

title: Diffusion in quantum system-reservoir models


We treat the following question: Consider a quantum particle on a lattice coupled to a thermal reservoir consisting of free bosons. Common wisdom suggests that, if the temperature of the reservoir is strictly positive, the particle diffuses. Up to now, we can prove this in two cases (both assuming that the coupling between particle and reservoir is weak):
1) If we replace the thermal reservoir by independent reservoirs at each lattice site (arXiv:0810.4537);
2) If the space dimension is higher than 4, the particle is heavy and it has some internal degrees of freedom (e.g. spin) which provide additional coupling to the field.
We will also discuss the relation of this problem to the question of kinetic and diffusive scaling limits for quantum particles, in particular the recent results by Erdos, Yau and Salmhofer (arXiv:math-ph/0512014). Time permitting, also the relation with quantum master equations will be discussed.


Mark Kac Seminar 2008-2009


last updated: 19 nov 2008by Markus