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The approach to equilibrium in quantum random walks

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  • Godoy, Salvador
  • Braun, E.

Abstract

We use the quantum random walk (QRW) model to build a quantum kinetic theory of diffusion in a one-dimensional, crystalline lattice, with a fixed number of cells. QRW is a reversible model and the quantum interferences are responsible for the process not satisfying an H-theorem. The microscopic entropy which increases statistically not dynamically, shows very large fluctuations. In the long-time limit, the entropy still fluctuates around some mean value, but in the limit of a large number of lattice cell, the relative fluctuations become negligible, allowing for the definition of thermodynamic equilibrium.

Suggested Citation

  • Godoy, Salvador & Braun, E., 1994. "The approach to equilibrium in quantum random walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 203(3), pages 414-424.
    • Handle: RePEc:eee:phsmap:v:203:y:1994:i:3:p:414-424
    DOI: 10.1016/0378-4371(94)90007-8
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    References listed on IDEAS

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    1. Balakrishnan, V., 1985. "Anomalous diffusion in one dimension," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 132(2), pages 569-580.
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