File
Authors
Ooshida, Takeshi Department of Mechanical and Physical Engineering, Tottori University Researchers DB KAKEN
Otsuki, Michio Graduate School of Engineering Science, Osaka University
Keywords
single-file diffusion
displacement correlation
fuctuation-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 fluctuations in colloidal systems. In the equilibrium case, the time-dependent Einstein relation holds between the two-tag displacement correlation and the response function corresponding to it, which is a manifestation of the fluctuation–dissipation theorem for the correlation of density fluctuations. While the standard procedure of closure approximation for nonlinear density fluctuations is known to be obstructed by inconsistency with the fluctuation–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) fluctuations and the corresponding response function, which is valid even if the system is out of equilibrium. This non-equilibrium fluctuation–response relation can be extended to the case of nonlinear fluctuations by means of closure approximation for the vacancy field.
Publisher
IOP Publishing
Content Type
Journal Article
Link
ISSN・ISBN
1361648X
NCID
AA12471247
Journal Title
Journal of physics. Condensed matter
Volume
30
Issue
37
Start Page
374001
Published Date
2018-08-21
Publisher-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