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arXiv · 1702.02099

Fokker-Planck formalism approach to Kibble-Zurek scaling laws and non-equilibrium dynamics

Ricardo Puebla·Ramil Nigmatullin·Tanja E. Mehlstäubler·Martin. B. Plenio
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Abstract

We study the non-equilibrium dynamics of second-order phase transitions in a simplified Ginzburg-Landau model using the Fokker-Planck formalism. In particular, we focus on deriving the Kibble-Zurek scaling laws that dictate the dependence of spatial correlations on the quench rate. In the limiting cases of overdamped and underdamped dynamics, the Fokker-Planck method confirms the theoretical predictions of the Kibble-Zurek scaling theory. The developed framework is computationally efficient, enables the prediction of finite-size scaling functions and is applicable to microscopic models as well as their hydrodynamic approximations. We demonstrate this extended range of applicability by analyzing the non-equilibrium linear to zigzag structural phase transition in ion Coulomb crystals confined in a trap with periodic boundary conditions.

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Ricardo Puebla, Ramil Nigmatullin, Tanja E. Mehlstäubler, Martin. B. Plenio. 2017-02-07. Fokker-Planck formalism approach to Kibble-Zurek scaling laws and non-equilibrium dynamics. https://doi.org/10.1103/physrevb.95.134104

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