On the Brownian gas: a field theory with a Poissonian ground state

Details On the Brownian gas: a field theory with a Poissonian ground state On the Brownian gas: a field theory with a Poissonian ground state

2008-02-21

arxiv.org/abs/0802.3212v1

J.Phys.A41:235002,2008

Physics

Condensed Matter

Statistical Mechanics

31 pages

Scientific paper

10.1088/1751-8113/41/23/235002

As a first step towards a successful field theory of Brownian particles in interaction, we study exactly the non-interacting case, its combinatorics and its non-linear time-reversal symmetry. Even though the particles do not interact, the field theory contains an interaction term: the vertex is the hallmark of the original particle nature of the gas and it enforces the constraint of a strictly positive density field, as opposed to a Gaussian free field. We compute exactly all the n-point density correlation functions, determine non-perturbatively the Poissonian nature of the ground state and emphasize the futility of any coarse-graining assumption for the derivation of the field theory. We finally verify explicitly, on the n-point functions, the fluctuation-dissipation theorem implied by the time-reversal symmetry of the action.

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