Advertisement

Journal of Statistical Physics

, Volume 175, Issue 2, pp 402–417 | Cite as

Particle Model for the Reservoirs in the Simple Symmetric Exclusion Process

  • Thu Dang Thien NguyenEmail author
Article
  • 52 Downloads

Abstract

In this paper, we will study the long time behavior of the simple symmetric exclusion process in the “channel” \(\varLambda _N=[1,N]\cap \mathbb {N}\) with reservoirs at the boundaries. These reservoirs are also systems of particles which can be exchanged with the particles in the channel. The size M of each reservoir is much larger than the one of the channel, i.e. \(M=N^{1+\alpha }\) for a fixed number \(\alpha >0\). Based on the size of the channel and the holding time at each reservoir, we will investigate some types of rescaling time.

Keywords

Hydrodynamic limits Adiabatic limits Ideal reservoir limits Global equilibrium limits 

Notes

Acknowledgements

I am truly grateful to Prof. Errico Presutti for providing me with so many worthwhile suggestions and helpful advices throughout discussion sessions.

References

  1. 1.
    Amir, M.: Sticky Brownian motion as the strong limit of a sequence of random walks. Stoch. Process. Appl. 39(2), 221–237 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    De Masi, A., Olla, S.: Quasi-static hydrodynamic limits. J. Stat. Phys. 161(5), 1037–1058 (2015)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Galves, A., Kipnis, C., Marchioro, C., Presutti, E.: Non equilibrium measures which exhibit a temperature gradient: study of a model. Commun. Math. Phys. 81, 124–147 (1981)ADSCrossRefzbMATHGoogle Scholar
  4. 4.
    Howitt, C. J.: Stochastic flows and sticky Brownian motion. PhD Thesis, The University of Warwick (2007)Google Scholar
  5. 5.
    Nguyen, T.D.T.: Fick law and sticky Brownian motions. J. Stat. Phys. 174, 494–518 (2018).  https://doi.org/10.1007/s10955-018-2190-y ADSMathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Gran Sasso Science InstituteL’AquilaItaly
  2. 2.Department of MathematicsUniversity of QuynhonQuy NhonVietnam

Personalised recommendations