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arXiv 1004.0412cond-mat.stat-mechmath-phmath.MP
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一类Hamilton模型的非平衡稳态

Nonequilibrium Steady States for Certain Hamiltonian Models

Kevin K. Lin, Lai-Sang Young

摘要:

本文报道了一类哈密顿模型的非平衡稳态的数值研究结果。在这些物质-能量耦合传输模型中,粒子通过与固定的旋转圆盘碰撞来交换能量。在[Commun. 262(2006)],Eckmann和Young研究了一维链,并表明某些简单的公式给出了能量和粒子密度分布的极好近似。保持[Eckmann-Young]中相互作用的基本模式,我们将他们的预测方案扩展到一些新的设置:不同晶格上的2D系统,由各种边界(热浴)条件驱动,包括使用恒温器。相同类型的粒子守恒模型表现出类似的行为。本文的后半部分研究了记忆和有限大小效应,这些效应似乎对[Eckmann-Young]中测试的模型的配置文件影响很小。我们证明,这些影响可以是显着的或微不足道的,这取决于当地的几何形状。动力学机制提出,并在粒子轨迹的方向性偏差的情况下,由于内存,校正方案的推导,并给出准确的预测。

英文摘要:

We report the results of a numerical study of nonequilibrium steady states for a class of Hamiltonian models. In these models of coupled matter-energy transport, particles exchange energy through collisions with pinned-down rotating disks. In [Commun. Math. Phys. 262 (2006)], Eckmann and Young studied 1D chains and showed that certain simple formulas give excellent approximations of energy and particle density profiles. Keeping the basic mode of interaction in [Eckmann-Young], we extend their prediction scheme to a number of new settings: 2D systems on different lattices, driven by a variety of boundary (heat bath) conditions including the use of thermostats. Particle-conserving models of the same type are shown to behave similarly. The second half of this paper examines memory and finite-size effects, which appear to impact only minimally the profiles of the models tested in [Eckmann-Young]. We demonstrate that these effects can be significant or insignificant depending on the local geometry. Dynamical mechanisms are proposed, and in the case of directional bias in particle trajectories due to memory, correction schemes are derived and shown to give accurate predictions.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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