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From Particle Systems to Partial Differential Equations II pp 355–370Cite as

Diffusion Coefficient for the Disordered Harmonic Chain Perturbed by an Energy Conserving Noise

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Abstract

We investigate the macroscopic behavior of the disordered harmonic chain of oscillators, through energy diffusion. The hamiltonian dynamics of the disordered system is perturbed by a degenerate conservative noise. After rescaling space and time diffusively, energy fluctuations in equilibrium evolve according to a linear heat equation (Simon, Equilibrium fluctuations for the disordered harmonic chain perturbed by an energy conserving noise, 2013). Here we concentrate on the diffusion coefficient, given by the non-gradient Varadhan’s approach, and equivalently defined through the Green-Kubo formula. We compare the two approaches and investigate the convergence of the diffusion coefficient in a vanishing noise limit.

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Acknowledgments

This problem was suggested by Cédric Bernardin, and I am grateful to him for helpful and valuable remarks. I warmly thank Makiko Sasada and Stefano Olla for their interest and constructive discussions on this work.

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Authors and Affiliations

  1. Departamento de Matemática, PUC, Rua Marquês de São Vicente 225, Rio de Janeiro, 22453-900, Brazil

    Marielle Simon

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  1. Marielle Simon
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Correspondence to Marielle Simon .

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Editors and Affiliations

  1. Centre of Mathematics, University of Minho, Braga, Portugal

    Patrícia Gonçalves

  2. Centre of Mathematics, University of Minho, Braga, Portugal

    Ana Jacinta Soares

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Simon, M. (2015). Diffusion Coefficient for the Disordered Harmonic Chain Perturbed by an Energy Conserving Noise. In: Gonçalves, P., Soares, A. (eds) From Particle Systems to Partial Differential Equations II. Springer Proceedings in Mathematics & Statistics, vol 129. Springer, Cham. https://doi.org/10.1007/978-3-319-16637-7_14

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