摘要翻译：
我们研究了一维(1D)颗粒链的热导率和体积粘度，该链具有三次+四次颗粒间势，没有现场势。该系统在其参数空间的一个子集上等价于FPU-Alpha-Beta系统。我们确定了三个不同的频率区，我们称之为流体动力区、微扰区和无碰撞区。在最低频率区（流体力学区），热量通过长波长声模式进行弹道传输。我们用来描述这种行为的模型预测，当频率为零时，与频率相关的体粘度和与频率相关的导热系数将以与频率相同的幂律依赖而发散。因此，我们可以将本体普朗特数定义为本体粘度与导热系数的比值（加上适当的前置因素使其无量纲化）。当频率为零时，这个无量纲比应该接近一个常值。我们用模式耦合理论来预测零频率极限。从模拟得到的大普朗特数的值与这些预测在广泛的系统参数范围内是一致的。在中频区，我们称之为微扰区，热量由四声子过程阻尼的声模传输。我们称最高频率区为无碰撞区，因为在这些频率下，观测时间比声子的特征弛豫时间短得多。在附录中详细讨论了微扰态和无碰撞态。
---
英文标题：
《Detailed Examination of Transport Coefficients in Cubic-Plus-Quartic
  Oscillator Chains》
---
作者：
G. R. Lee-Dadswell, B. G. Nickel, C. G. Gray
---
最新提交年份：
2007
---
分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
--

---
英文摘要：
  We examine the thermal conductivity and bulk viscosity of a one-dimensional (1D) chain of particles with cubic-plus-quartic interparticle potentials and no on-site potentials. This system is equivalent to the FPU-alpha beta system in a subset of its parameter space. We identify three distinct frequency regimes which we call the hydrodynamic regime, the perturbative regime and the collisionless regime. In the lowest frequency regime (the hydrodynamic regime) heat is transported ballistically by long wavelength sound modes. The model that we use to describe this behaviour predicts that as the frequency goes to zero the frequency dependent bulk viscosity and the frequency dependent thermal conductivity should diverge with the same power law dependence on frequency. Thus, we can define the bulk Prandtl number as the ratio of the bulk viscosity to the thermal conductivity (with suitable prefactors to render it dimensionless). This dimensionless ratio should approach a constant value as frequency goes to zero. We use mode-coupling theory to predict the zero frequency limit. Values of the bulk Prandtl number from simulations are in agreement with these predictions over a wide range of system parameters. In the middle frequency regime, which we call the perturbative regime, heat is transported by sound modes which are damped by four-phonon processes. We call the highest frequency regime the collisionless regime since at these frequencies the observing times are much shorter than the characteristic relaxation times of phonons. The perturbative and collisionless regimes are discussed in detail in the appendices.
---
PDF链接：
https://arxiv.org/pdf/710.1066