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On the stationary measures of anharmonic systems in the presence of a small thermal noise

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Abstract

We consider certain small stochastic perturbations of ad-dimensional infinite system of coupled anharmonic oscillators. The evolution law is reversible in the Yaglom sense, thus Gibbs states with the given interaction and temperature are stationary measures. If d<3 then some stability properties of the interaction imply the converse statement; if d>2 then the same is proven for translation invariant measures only. The methods and results of Ref. 4, 6–8 are extended to second-order systems of stochastic differential equations.

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  1. Mathematical Institute, HAS, POB 127, H-1364, Budapest, Hungary

    J. Fritz

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  1. J. Fritz
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Fritz, J. On the stationary measures of anharmonic systems in the presence of a small thermal noise. J Stat Phys 44, 25–47 (1986). https://doi.org/10.1007/BF01010903

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