Laplacians, Random Walks, Bose Gas, Quantum Spin Systems
We investigate Brownian motion and Laplacians in various geometries, their interplay with quantum spin/particle systems, with particular emphasis on phase transitions, long range order, Bose-Einstein condensation. We also plan to investigate related problems of asymptotics and scaling of random processes with path-wise self-interaction, exploit the power of stochastic representations of quantum systems. Special emphasis will be put on the interdisciplinary (mathematics/physics) aspects of the project. Senior participants at all nodes have remarkable record in these investigations. In joining their expertise, we will lead to new and efficient approaches to these fundamental and difficult problems.
Balint Toth - University of Bristol/ Budapest
Fionnuala Hill - University of Bristol