Geodesic
Analytic approach to the~(an)harmonic crystal chains with
Teoretičeskaâ i matematičeskaâ fizika, Tome 156 (2008) no. 1, pp. 138-146

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We consider the harmonic and anharmonic chains of oscillators with self-consistent stochastic reservoirs and derive an integral representation (à la Feynman–Kac) for the correlations, in particular, for the heat flow. For the harmonic chain, we give a new proof that its thermal conductivity is finite in the steady state. Based on this integral representation for the correlations and a perturbative analysis, the approach is quite general and can be extended to more intricate systems.
Keywords: harmonic crystal, anharmonic crystal, stochastic reservoirs, heat flow. 
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     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2008_156_1_a7/}
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R. Falcao; A. Francisco Neto; E. Pereira. Analytic approach to the~(an)harmonic crystal chains with. Teoretičeskaâ i matematičeskaâ fizika, Tome 156 (2008) no. 1, pp. 138-146. http://geodesic.mathdoc.fr/item/TMF_2008_156_1_a7/