Jansen, Sabine, Konig, Wolfgang, Schmidt, Bernd and Theil, Florian (2021) Surface energy and boundary layers for a chain of atoms at low temperature. Archive for Rational Mechanics and Analysis, 239 . pp. 915-980. doi:10.1007/s00205-020-01587-3 ISSN 0003-9527.

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Abstract

We analyze the surface energy and boundary layers for a chain of atoms at low temperature for an interaction potential of Lennard–Jones type. The pressure (stress) is assumed to be small but positive and bounded away from zero, while the temperature \beta ^{-1} goes to zero. Our main results are: (1) As \beta \rightarrow \infty at fixed positive pressure p>0, the Gibbs measures \mu _\beta and \nu _\beta for infinite chains and semi-infinite chains satisfy path large deviations principles. The rate functions are bulk and surface energy functionals \overline{{\mathcal {E}}}_{\mathrm {bulk}} and \overline{{\mathcal {E}}}_\mathrm {surf}. The minimizer of the surface functional corresponds to zero temperature boundary layers; (2) The surface correction to the Gibbs free energy converges to the zero temperature surface energy, characterized with the help of the minimum of \overline{{\mathcal {E}}}_\mathrm {surf}; (3) The bulk Gibbs measure and Gibbs free energy can be approximated by their Gaussian counterparts; (4) Bounds on the decay of correlations are provided, some of them uniform in \beta .

Item Type:	Journal Article
Alternative Title:
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title:	Archive for Rational Mechanics and Analysis
Publisher:	Springer
ISSN:	0003-9527
Official Date:	February 2021
Dates:	Date Event February 2021 Published 21 December 2020 Available 2 October 2020 Accepted
Volume:	239
Page Range:	pp. 915-980
DOI:	10.1007/s00205-020-01587-3
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access (Creative Commons)
Date of first compliant deposit:	23 October 2020
Date of first compliant Open Access:	22 December 2020
Related URLs:	Publisher
Open Access Version:	ArXiv

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