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Partially asymmetric zero-range process with quenched disorder.

Róbert Juhász1, Ludger Santen, Ferenc Iglói

  • 1Fachrichtung Theoretische Physik, Universität des Saarlandes, D-66041 Saarbrücken, Germany. juhasz@lusi.uni-sb.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 31, 2005
PubMed
Summary

Disordered zero-range processes exhibit particle condensation. Transport dynamics depend on the dynamical exponent z, with distinct mechanisms for active and inactive particles.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Stochastic Processes

Background:

  • The one-dimensional partially asymmetric zero-range process is a key model for studying particle transport in disordered systems.
  • Disorder in hopping rates and direction can lead to complex phenomena like particle condensation.

Purpose of the Study:

  • To investigate the steady-state properties of a one-dimensional partially asymmetric zero-range process with random hopping rates and easy direction.
  • To characterize the condensation phenomenon and the transport mechanisms in the presence of strong disorder.

Main Methods:

  • Extreme value statistics
  • Asymptotically exact strong disorder renormalization group method
  • Calculation of the dynamical exponent (z)

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Main Results:

  • A condensation phenomenon is observed in the thermodynamic limit, where particles occupy a single site.
  • The system's current vanishes as J ~ L(-z), with z exactly calculated.
  • Two distinct transport regimes identified: active particles for 0 < z < 1 and anomalous diffusion for z > 1.
  • Inactive particles localize, and their density profile width scales as xi ~ delta(-2).
  • Condensate size grows as n(L) ~ t(1/(1+z)) during the coarsening process.

Conclusions:

  • The study provides an exact calculation of the dynamical exponent for this disordered system.
  • The findings reveal distinct particle transport mechanisms governed by the degree of disorder.
  • The coarsening dynamics towards the steady state are characterized, showing a power-law growth of the condensate size.