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A class of mass transport models: Factorised steady states and condensation in real space: Lecture II

Presented by: 
SN Majumdar Université Paris-Sud
Wednesday 29th March 2006 - 11:30 to 12:30
INI Seminar Room 1


The traditional Bose-Einstein condensation in an ideal quantum Bose gas occurs in momentum space, when a macroscopically large number of bosons condense onto the ground state. It is becoming increasingly clear over the last decade that condensation can also happen in real space (and even in one dimension) in the steady state of a broad class of physical systems. These are classical systems, generally lack a Hamiltonian and are defined by their microscopic kinetic processes. Examples include traffic jams on a highway, island formation on growing crystals and many other systems. In this lecture, I'll discuss in detail two simple models namely the Zero-range process and the Chipping model that exhbits condensation in real space. Lecture-II

I'll introduce a generalized mass transport model that includes in iteself, as specail cases, the Zero-range process, the Chipping model and the Random Average process. We will derive a necessary and sufficient condition, in one dimension, for the model to have a factorised steady state. Generalization to arbitrary graphs will be mentioned also.


We will discuss, in the context of the mass transport model, the phenomenon of condensation. In particular we will address three basic isuues: (1) WHEN does such a condensation occur (the criterion) (2) HOW does the condensation happen (the mechanism) and (3) WHAT does the condensate look like (the nature of fluctuations and lifetime of the condensate etc.)? We will see how these issues can be resolved analytically in the mass transport model.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons