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Condensation phenomena with distinguishable particles.

Jun Ohkubo1

  • 1Institute for Solid State Physics, University of Tokyo, Kashiwanoha 5-1-5, Kashiwa-shi, Chiba 277-8581, Japan. ohkubo@issp.u-tokyo.ac.jp

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Summary

This study explores condensation in classical stochastic processes like the Ehrenfest class. Quenched disorder is key to condensation in preferential urn models, showing three distinct types.

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Area of Science:

  • Statistical mechanics
  • Stochastic processes
  • Complex systems

Background:

  • Classical stochastic processes, including zero-range and urn models, exhibit complex behaviors.
  • The Ehrenfest class of stochastic processes, analogous to Maxwell-Boltzmann statistics, involves distinguishable particles.
  • Understanding condensation phenomena in disordered systems is crucial for statistical mechanics.

Purpose of the Study:

  • To analytically investigate the conditions for condensation in disordered classical stochastic processes within the Ehrenfest class.
  • To examine the role of quenched disorder in condensation phenomena, specifically in preferential urn models.
  • To identify and characterize different types of condensation in disordered urn models.

Main Methods:

  • Analysis of site-particle systems, including zero-range processes and urn models.
  • Mathematical treatment of stochastic processes in the Ehrenfest class.
  • Investigation of disordered systems, focusing on the preferential urn model.

Main Results:

  • Analytical conditions for condensation phenomena in disordered Ehrenfest class processes were established.
  • The crucial role of quenched disorder in enabling condensation within the preferential urn model was demonstrated.
  • Three distinct condensation patterns were identified in the preferential urn model, contingent on disorder parameters.

Conclusions:

  • Disordered classical stochastic processes, particularly within the Ehrenfest class, can exhibit condensation.
  • Quenched disorder is a significant factor driving condensation in preferential urn models.
  • The preferential urn model serves as a valuable case study for understanding disorder-induced condensation in stochastic systems.