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On Time Correlations for KPZ Growth in One Dimension
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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On Time Correlations for KPZ Growth in One Dimension
Інший ID:
2010 Mathematics Subject Classification: 60K35; 82C22; 82B43
DOI:10.3842/SIGMA.2016.074
DOI:10.3842/SIGMA.2016.074
Посилання:
On Time Correlations for KPZ Growth in One Dimension / P.L. Ferrari, H. Spohn // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 50 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Asymptotics and Universality in Random Matrices,
Random Growth Processes, Integrable Systems and Statistical Physics in honor of Percy Deift and Craig Tracy.
The full collection is available at http://www.emis.de/journals/SIGMA/Deift-Tracy.html.
gements
The work of P.L. Ferrari is supported by the German Research Foundation via the SFB 1060–
B04 project. The final version of our contribution was written when both of us visited in
early 2016 the Kavli Institute of Theoretical Physics at Santa Barbara. The research stay
of H. Spohn at KITP is supported by the Simons Foundation. This research was supported
in part by the National Science Foundation under Grant No. NSF PHY11-25915. We thank
Kazumasa Takeuchi for illuminating discussions on the comparison with his experimental results
and Joachim Krug for explaining to us earlier work on time correlations.
Дата:
2016
Переглядів:
477
Завантажень:
216
Анотація:
Time correlations for KPZ growth in 1+1 dimensions are reconsidered. We discuss flat, curved, and stationary initial conditions and are interested in the covariance of the height as a function of time at a fixed point on the substrate. In each case the power laws of the covariance for short and long times are obtained. They are derived from a variational problem involving two independent Airy processes. For stationary initial conditions we derive an exact formula for the stationary covariance with two approaches: (1) the variational problem and (2) deriving the covariance of the time-integrated current at the origin for the corresponding driven lattice gas. In the stationary case we also derive the large time behavior for the covariance of the height gradients.
