Abstract
This is a short survey on recent results obtained by the authors on dynamical phase transitions of interacting particle systems. We consider particle systems with exclusion dynamics, but it is conjectured that our results should hold for a general class of particle systems. The parameter giving rise to the phase transition is the “slowness” of a single bond in the discrete lattice. The phase transition is verified not only in the hydrodynamics, but also in the fluctuations of the density, the current and the tagged particle. Moreover, we found a phase transition in the continuum, that is, at the level of the hydrodynamic equations, in agreement with the dynamical phase transition for the particle systems.
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Acknowledgements
The authors thank the great hospitality of CMAT (Portugal), IMPA and PUC (Rio de Janeiro).
A.N. thanks Cnpq (Brazil) for support through the research project “Mecânica estatística fora do equilíbrio para sistemas estocásticos” Universal n. 479514/2011-9.
P.G. thanks FCT (Portugal) for support through the research project “Non-Equilibrium Statistical Physics” PTDC/MAT/109844/2009. P.G. thanks the Research Centre of Mathematics of the University of Minho, for the financial support provided by “FEDER” through the “Programa Operacional Factores de Competitividade COMPETE” and by FCT through the research project PEst-C/MAT/UI0013/2011.
T.F. was supported through a grant “BOLSISTA DA CAPES - Braslia/Bra-sil” provided by CAPES (Brazil).
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Franco, T., Gonçalves, P., Neumann, A. (2014). Slowed Exclusion Process: Hydrodynamics, Fluctuations and Phase Transitions. In: Bernardin, C., Gonçalves, P. (eds) From Particle Systems to Partial Differential Equations. Springer Proceedings in Mathematics & Statistics, vol 75. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54271-8_8
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DOI: https://doi.org/10.1007/978-3-642-54271-8_8
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