The Structure of Langevin's Memory Kernel From Lagrangian Dynamics

Details The Structure of Langevin's Memory Kernel From Lagrangian Dynamics The Structure of Langevin's Memory Kernel From Lagrangian Dynamics

2000-12-13

arxiv.org/abs/cond-mat/0012230v1

Europhys. Lett., 50 (5), pp. 628-634 (2000)

Physics

Condensed Matter

Statistical Mechanics

8 pages, 5 figures, latex, include europhys.sty and euromacr.tex

Scientific paper

10.1209/epl/i2000-00316-7

We obtain the memory kernel of the generalized Langevin equation, describing a particle interacting with longitudinal phonons in a liquid. The kernel is obtained analytically at T=0 Kelvin and numerically at T>0 Kelvin. We find that it shows some non-trivial structural features like negative correlations for some range of time separations. The system is shown to have three characteristic time scales, that control the shape of the kernel, and the transition between quadratic and linear behavior of the mean squared distance (MSD). Although the derivation of the structure in the memory kernel is obtained within a specific dynamical model, the phenomenon is shown to be quite generic.

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