The Einstein Relation for the KPZ Equation

被引：4

作者：

Goncalves, Patricia ^{[1
,2
]}

Jara, Milton ^{[3
]}

机构：

[1] Pontificia Univ Catolica Rio de Janeiro, Dept Matemat, BR-22453900 Rio de Janeiro, RJ, Brazil

[2] Univ Minho, Ctr Matemat, CMAT, P-4710057 Braga, Portugal

[3] IMPA, BR-22460340 Rio De Janeiro, Brazil

来源：

JOURNAL OF STATISTICAL PHYSICS | 2015年 / 158卷 / 06期

关键词：

KPZ equation; Gradient Kawasaki dynamics; Equilibrium fluctuations; Einstein relation; FLUCTUATIONS; PROBABILITY;

D O I：

10.1007/s10955-014-1158-9

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We compute the non-universal constants in the KPZ equation in one dimension, in terms of the thermodynamical quantities associated to the underlying microscopic dynamics. In particular, we derive the second-order Einstein relation for the transport coefficient of the KPZ equation, in terms of the conserved quantity , the diffusion coefficient , the strength of the asymmetry and the static compressibility of the system chi.

引用

页码：1262 / 1270

页数：9

共 21 条

[1] Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 Dimensions
Amir, Gideon
Corwin, Ivan
Quastel, Jeremy
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2011, 64 (04) : 466 - 537
[2] On the distribution of the length of the longest increasing subsequence of random permutations
Baik, J
Deift, P
Johansson, K
[J]. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 12 (04) : 1119 - 1178
[3] Stochastic burgers and KPZ equations from particle systems
Bertini, L
Giacomin, G
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1997, 183 (03) : 571 - 607
[4] LARGE DEVIATION PRINCIPLES FOR NONGRADIENT WEAKLY ASYMMETRIC STOCHASTIC LATTICE GASES
Bertini, Lorenzo
Faggionato, Alessandra
Gabrielli, Davide
[J]. ANNALS OF APPLIED PROBABILITY, 2013, 23 (01) : 1 - 65
[5] Integrable probability: From representation theory to Macdonald processes
Borodin, Alexei
Petrov, Leonid
[J]. PROBABILITY SURVEYS, 2014, 11 : 1 - 58
[6] EQUILIBRIUM FLUCTUATIONS OF STOCHASTIC PARTICLE-SYSTEMS - THE ROLE OF CONSERVED QUANTITIES
BROX, T
ROST, H
[J]. ANNALS OF PROBABILITY, 1984, 12 (03) : 742 - 759
[7] THE KARDAR-PARISI-ZHANG EQUATION AND UNIVERSALITY CLASS
Corwin, Ivan
[J]. RANDOM MATRICES-THEORY AND APPLICATIONS, 2012, 1 (01)
[8] DEMASI A, 1986, ANN PROBAB, V14, P409
[9] Goncalves P., ANN PROBABI IN PRESS
[10] Nonlinear Fluctuations of Weakly Asymmetric Interacting Particle Systems
Goncalves, Patricia
Jara, Milton
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2014, 212 (02) : 597 - 644

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