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Condensation and metastability in the zero-range process. Paul Chleboun Stefan Grosskinsky Complexity Forum 27/10/2010. The big idea. We use general techniques such as; Large deviations and entropy methods. To help our understanding of;

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condensation and metastability in the zero range process

Condensation and metastability in the zero-range process

Paul Chleboun

Stefan Grosskinsky

Complexity Forum

27/10/2010

the big idea
The big idea
  • We use general techniques such as;
    • Large deviations and entropy methods.
  • To help our understanding of;
    • condensation in non equilibrium statistical mechanics.
  • Demonstrate methods
    • by application to a simple toy model.
motivation
Motivation
  • What is condensation & why do we care?
motivation1
Motivation
  • What is condensation & why do we care?
  • 1) Traffic jams.
motivation2
Motivation
  • 2) In granular media.
the zero range process
The zero range process

[Spitzer (1970), Evans (2000)]

stationary measures grand canonical
Stationary measuresGrand canonical
  • A family of stationary product measures

Single site weights:

stationary measures canonical
Stationary measuresCanonical
  • Dynamics conserve total number of particles
  • Fixed L and N the system is irreducible and finite state so ergodic.
condensation transition
Condensation transition

[van der Meer, van der Weele, Lohse, Mikkelsen, Versluis (2001-02)]

condensation transition1
Condensation transition
  • Example:

[Grosskinsky, Schuetz, Spohn (2003)]

canonical distribution of the maximum
Canonical distribution of the maximum
  • How does the condensate move?
canonical distribution of the maximum1
Canonical distribution of the maximum
  • Rate function for maximum
remarks
Remarks
  • We have developed a general approach to studying the condensation transition.
  • Very useful methods for calculating lifetimes of states using simple current and entropy calculations.
  • The large deviation results are helpful in understanding the dynamics.
  • Size Dependent systems help us to understand finite size effects in non-size dependent systems.
acknowledgements
Acknowledgements

Thanks to:

  • EPSRC for funding.
  • Many people in the Complexity DTC, staff and students, for helpful discussion.

Thank you for listening!

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  • Sorry for the rush.
  • If you are interested and want to here more details (and the things I didn’t have time for) then...

Probability forum:

Wed, Nov 10 (2 weeks) at 12pm in A1.01 Zeeman building