Andrea Velenich et al 2008 J. Phys. A: Math. Theor. 41 235002 doi:10.1088/1751-8113/41/23/235002
On the Brownian gas: a field theory with a Poissonian ground state
Andrea Velenich1, Claudio Chamon1, Leticia F Cugliandolo2 and Dirk Kreimer3,4
Show affiliationsAs a first step toward a successful field theory of Brownian particles in interaction, we study exactly the non-interacting case, its combinatorics and nonlinear 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.
- PACS
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02.50.Ng Distribution theory and Monte Carlo studies
- MSC
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05Cxx Graph theory (For applications of graphs, see 68R10, 90C35, 94C15)
- Subjects
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Soft matter, liquids and polymers
- Dates
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Issue 23 (13 June 2008)
Received 21 February 2008, in final form 23 April 2008
Published 19 May 2008
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On the Brownian gas: a field theory with a Poissonian ground state
Andrea Velenich et al 2008 J. Phys. A: Math. Theor. 41 235002
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