Andrea Velenich et al 2008 J. Phys. A: Math. Theor. 41 235002 doi:10.1088/1751-8113/41/23/235002
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.
02.50.Ng Distribution theory and Monte Carlo studies
05Cxx Graph theory (For applications of graphs, see 68R10, 90C35, 94C15)
Soft matter, liquids and polymers
Issue 23 (13 June 2008)
Received 21 February 2008, in final form 23 April 2008
Published 19 May 2008
Andrea Velenich et al 2008 J. Phys. A: Math. Theor. 41 235002
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