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

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...

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Bibliographic Details
Published in:arXiv.org 2008-02
Main Authors: Velenich, Andrea, Chamon, Claudio, Cugliandolo, Leticia F, Kreimer, Dirk
Format: Article
Language:English
Subjects:
Brownian motion
Combinatorial analysis
Density
Field theory
Granulation
Ground state
Magnetic fields
Symmetry
Variation
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.0802.3212