Authors
Ooshida, Takeshi Department of Mechanical and Physical Engineering, Tottori University Tottori University Researchers KAKEN Search Researchers
Otsuki, Michio Graduate School of Engineering Science, Osaka University
Keywords
single-file diffusion
displacement correlation
uctuation-response relation
Einstein relation
Dean-Kawasaki equation
mode-coupling theory
ageing
Abstract
Spatiotemporally correlated motions of interacting Brownian particles, confined in a narrow channel of infinite length, are studied in terms of statistical quantities involving two particles. A theoretical framework that allows analytical calculation of two-tag correlations is presented on the basis of the Dean-Kawasaki equation describing density uctuations in colloidal systems. In the equilibrium case, the time-dependent Einstein relation holds between the two-tag displacement correla- tion and the response function corresponding to it, which is a manifestation of the uctuation-dissipation theorem for the correlation of density uctuations. While the standard procedure of closure approximation for nonlinear density uctuations is known to be obstructed by inconsistency with the uctuation-dissipation theorem, this difficulty is naturally avoided by switching from the standard Fourier representation of the density field to the label-based Fourier representation of the vacancy field. In the case of ageing dynamics started from equidistant lattice configuration, the time-dependent Einstein relation is violated, as the two-tag correlation depends on the waiting time for equilibration while the response function is not sensitive to it. Within linear approximation, however, there is a simple relation between the density (or vacancy) uctuations and the corresponding response function, which is valid even if the system is out of equilibrium. This non-equilibrium uctuation-response relation can be extended to the case of nonlinear uctuations by means of closure approximation for the vacancy field.
Publisher
IOP Publishing
Content Type
Journal Article
Link
http://iopscience.iop.org/article/10.1088/1361-648X/aad4cc
ISSN・ISBN
1361648X
NCID
AA12471247
Journal Title
Journal of physics. Condensed matter
Current Journal Title
Journal of physics. Condensed matter
Volume
30
Issue
37
Start Page
374001
Published Date
2018-08-21
DOI
Text Version
Author
Rights
© 2018 IOP Publishing Ltd
Citation
This work was published by IOP Publishing.: Takeshi Ooshida and Michio Otsuki. Two-tag correlations and nonequilibrium fluctuation–response relation in ageing single-file diffusion. Journal of Physics: Condensed Matter. 2018, 30(37), 374001. DOI: https://doi.org/10.1088/1361-648X/aad4cc
Department
Faculty of Engineering/Graduate School of Engineering
Language
English