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Exploratory behavior, trap models, and glass transitions.

Alexandre S Martinez1, Osame Kinouchi, Sebastian Risau-Gusman

  • 1Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto, Universidade de São Paulo, Avenida Bandeirantes 3900, 14040-901 Ribeirão Preto, São Paulo, Brazil. martinez@dfm.ffclrp.usp.br

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 5, 2004
PubMed
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A random walk on a disordered landscape shows a glass transition at a critical temperature. Below this temperature, the system enters a long-lived, out-of-equilibrium state with aging effects.

Area of Science:

  • Statistical physics
  • Complex systems
  • Disordered systems

Background:

  • Random walks are fundamental models for diffusion and transport.
  • Disordered systems exhibit complex behaviors due to randomness.
  • Glass transitions mark transitions to non-equilibrium states.

Purpose of the Study:

  • To investigate the behavior of a random walk on a disordered landscape.
  • To identify phase transitions and critical phenomena in such systems.
  • To explore aging phenomena in out-of-equilibrium regimes.

Main Methods:

  • Performing a random walk on N sites in a d-dimensional hypercube.
  • Utilizing a hopping probability dependent on distance and temperature (beta = 1/T).
  • Analyzing the cost function E(D) = D(d) for analytic results.

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Main Results:

  • A glass transition occurs at a critical inverse temperature beta(d).
  • Below the critical temperature T(d), average trapping time diverges.
  • The system exhibits aging phenomena in the out-of-equilibrium regime.

Conclusions:

  • The model exhibits a temperature-driven glass transition.
  • Out-of-equilibrium dynamics and aging are characteristic below T(d).
  • The study provides insights into Lévy flight scenarios and exploratory behavior.