The free Bose gas and permutations of integers

Add to your list(s) Download to your calendar using vCal

• Thomas Richthammer (Munich)
• Tuesday 15 January 2013, 16:30-17:30
• MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.

If you have a question about this talk, please contact neb25.

Using Feynman’s representation, the equilibrium state of the Bose gas can be described in terms of a probabilistic model, similar to models from non-quantum statistical mechanics. In this model a particle configuration is characterized by the positions of the particles in combination with a permutation of the particles. The natural mathematical framework for such a particle model is an infinite volume description, but in the case of the Bose gas model this infinite volume description is still missing: The main difficulty here is to incorporate the particle permutations into the model.

In order to show how to overcome this difficulty we consider a toy model, where the particle positions are fixed at the vertices of the integer lattice. We introduce an infinite volume description of this model in terms of Gibbs measures on permutations of the integers. This model can then be analyzed by means of geometric tools (based on a quantity called the flux of a permutation) in combination with probability estimates and cut-block arguments.

Our result provides a full classification of possible states of the system: For every temperature there are infinitely many possible states, all of them are translation invariant, and exactly one of them is concentrated on permutations consisting of finite cycles only.

The talk is based on joint work with Marek Biskup (UCLA).

This talk is part of the Probability series.

This talk is included in these lists:

• All CMS events
• All Talks (aka the CURE list)
• CMS Events
• DPMMS Lists
• DPMMS info aggregator
• MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB
• Probability
• School of Physical Sciences
• Statistical Laboratory info aggregator

Note that ex-directory lists are not shown.