Driven tracer particle in one dimensional symmetric simple exclusion

被引:67
作者
Landim, C
Olla, S
Volchan, SB
机构
[1] IMPA, BR-22460 Rio De Janeiro, Brazil
[2] Univ Rouen, CNRS URA 1378, F-76128 Mt St Aignan, France
[3] Univ Cergy Pontoise, Dept Math, F-95302 Cergy Pontoise, France
[4] Ecole Polytech, Ctr Math Appl, F-91128 Palaiseau, France
关键词
D O I
10.1007/s002200050300
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
Consider an infinite system of particles evolving in a one dimensional lattice according to symmetric random walks with hard core interaction. We investigate the behavior of a tagged particle under the action of an external constant driving force. We prove that the diffusively rescaled position of the test particle epsilon X(epsilon(-2)t), t > 0, converges in probability, as epsilon --> 0, to a deterministic function v(t). The function v(.) depends on the initial distribution of the random environment through a non-linear parabolic equation. This law of large numbers for the position of the tracer particle is deduced from the hydrodynamical limit of an inhomogeneous one dimensional symmetric zero range process with an asymmetry at the origin, An Einstein relation is satisfied asymptotically when the external force is small.
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页码:287 / 307
页数:21
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