On Time Correlations for KPZ Growth in One Dimension
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...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2016 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2016
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147840 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-147840 |
|---|---|
| record_format |
dspace |
| spelling |
Ferrari, P.L. Spohn, H. 2019-02-16T09:11:13Z 2019-02-16T09:11:13Z 2016 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. 1815-0659 2010 Mathematics Subject Classification: 60K35; 82C22; 82B43 DOI:10.3842/SIGMA.2016.074 https://nasplib.isofts.kiev.ua/handle/123456789/147840 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On Time Correlations for KPZ Growth in One Dimension Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
On Time Correlations for KPZ Growth in One Dimension |
| spellingShingle |
On Time Correlations for KPZ Growth in One Dimension Ferrari, P.L. Spohn, H. |
| title_short |
On Time Correlations for KPZ Growth in One Dimension |
| title_full |
On Time Correlations for KPZ Growth in One Dimension |
| title_fullStr |
On Time Correlations for KPZ Growth in One Dimension |
| title_full_unstemmed |
On Time Correlations for KPZ Growth in One Dimension |
| title_sort |
on time correlations for kpz growth in one dimension |
| author |
Ferrari, P.L. Spohn, H. |
| author_facet |
Ferrari, P.L. Spohn, H. |
| publishDate |
2016 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147840 |
| citation_txt |
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. |
| work_keys_str_mv |
AT ferraripl ontimecorrelationsforkpzgrowthinonedimension AT spohnh ontimecorrelationsforkpzgrowthinonedimension |
| first_indexed |
2025-12-07T17:52:35Z |
| last_indexed |
2025-12-07T17:52:35Z |
| _version_ |
1850872908532940801 |