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An appetizer to modern developments on the Kardar–Parisi–Zhang universality class

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  • Takeuchi, Kazumasa A.

Abstract

The Kardar–Parisi–Zhang (KPZ) universality class describes a broad range of non-equilibrium fluctuations, including those of growing interfaces, directed polymers and particle transport, to name but a few. Since the year 2000, our understanding of the one-dimensional KPZ class has been completely renewed by mathematical physics approaches based on exact solutions. Mathematical physics has played a central role since then, leading to a myriad of new developments, but their implications are clearly not limited to mathematics — as a matter of fact, it can also be studied experimentally. The aim of these lecture notes is to provide an introduction to the field that is accessible to non-specialists, reviewing basic properties of the KPZ class and highlighting main physical outcomes of mathematical developments since the year 2000. It is written in a brief and self-contained manner, with emphasis put on physical intuitions and implications, while only a small (and mostly not the latest) fraction of mathematical developments could be covered. Liquid-crystal experiments by the author and coworkers are also reviewed.

Suggested Citation

  • Takeuchi, Kazumasa A., 2018. "An appetizer to modern developments on the Kardar–Parisi–Zhang universality class," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 504(C), pages 77-105.
    • Handle: RePEc:eee:phsmap:v:504:y:2018:i:c:p:77-105
    DOI: 10.1016/j.physa.2018.03.009
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    Citations

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    Cited by:

    1. Kim, Yujin H., 2021. "The lower tail of the half-space KPZ equation," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 365-406.
    2. Hu, Xiongpeng & Hao, Dapeng & Xia, Hui, 2023. "Improved finite-difference and pseudospectral schemes for the Kardar–Parisi–Zhang equation with long-range temporal correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 619(C).
    3. Muzzio, Nicolás E. & Horowitz, Claudio M. & Azzaroni, Omar & Moya, Sergio E. & Pasquale, Miguel A., 2021. "Tilted mammalian cell colony propagation dynamics on patterned substrates," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).

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