The toy-model of the Boltzmann type equation for the contact force distribution in disordered packings of particles

弱相互作用系统大集合中的Boltzmann熵和混沌

Boltzmann entropy and chaos in a large assembly of weakly interacting systems

我们引入了一个高维辛映射，模拟了一个由弱相互作用的混沌子系统组成的大系统，作为一个玩具模型来分析热力学系统中的单粒子混沌动力学和粒子相互作用之间的相互作用。我们研究了在这个系统中玻尔兹曼熵S_B随时间的增长作为粗粒化分辨率的函数。我们表明，出现一个特征尺度，S_B与t的行为，在与吉布斯熵的变化，不依赖于粗粒化的分辨率，只要它是比这个尺度更细。粒子间的相互作用是实现这一结果的关键，而熵增长的速率基本上取决于单粒子混沌动力学（t不太小）。这是可能的解释的动力学的基本特征，在一个合适的马尔可夫近似。

Damping of Bloch oscillations: Variational solutions of the Boltzmann equation beyond linear response

Variational solutions of the Boltzmann equation usually rely on the concept of linear response. We extend the variational approach for tight-binding models at high entropies to a regime far beyond linear response. We analyze both weakly interacting fermions and incoherent bosons on a lattice. We consider a case where the particles are driven by a constant force, leading to the well-known Bloch oscillations, and we consider interactions that are weak enough not to overdamp these oscillations. This regime is computationally demanding and relevant for ultracold atoms in optical lattices. We deriv…

Microcanonical Monte Carlo Study of One Dimensional Self-Gravitating Lattice Gas Models

In this study we present a Microcanonical Monte Carlo investigation of one dimensional self-gravitating toy models. We study the effect of hard-core potentials and compare to those results obtained with softening parameters and also the effect of the geometry of the models. In order to study the effect of the geometry and the borders in the system we introduce a model with the symmetry of motion in a line instead of a circle, which we denominate as $1/r$ model. The hard-core particle potential introduces the effect of the size of particles and, consequently, the effect of the density of the sy…

Relaxation of ideal classical particles in a one-dimensional box

We study the deterministic dynamics of non-interacting classical gas particles confined to a one-dimensional box as a pedagogical toy model for the relaxation of the Boltzmann distribution towards equilibrium. Hard container walls alone induce a uniform distribution of the gas particles at large times. For the relaxation of the velocity distribution we model the dynamical walls by independent scatterers. The Markov property guarantees a stationary but not necessarily thermal velocity distribution for the gas particles at large times. We identify the conditions for physical walls where the stat…

Dynamics of Fluid Mixtures in Nanospaces

A multicomponent extension of our recent theory of simple fluids [ U.M.B. Marconi and S. Melchionna, Journal of Chemical Physics, 131, 014105 (2009) ] is proposed to describe miscible and immiscible liquid mixtures under inhomogeneous, non steady conditions typical of confined fluid flows. We first derive from a microscopic level the evolution equations of the phase space distribution function of each component in terms of a set of self consistent fields, representing both body forces and viscous forces (forces dependent on the density distributions in the fluid and on the velocity distributio…

Kadanoff-Baym方程的随机解释及其与Langevin过程的关系

Stochastic interpretation of Kadanoff-Baym equations and their relation to Langevin processes

在这个更多的教学研究中，我们要阐明随机方面固有的（非）平衡实时格林函数描述（或“封闭的时间路径格林函数”- CTPGF）的传输方程，所谓的“Kadanoff-Baym方程”。作为一个玩具模型，我们将一个自由标量玻色子量子场耦合到一个给定温度T的热浴中。它将详细地表明，新兴的输运方程必须被理解为集合平均的随机方程的朗之万型。这对应于Feynman和Vernon的影响函数方法和CTP技术的等价性。然而，前者给出了一个更直观的物理图像。特别是（量子）噪声的物理作用和其相关内核的Kadanoff-Baym方程的连接将被讨论。由涨落耗散定理相关的噪声和耗散的固有存在保证了模式或粒子在长时间限制中平均变得热填充。对于动量远小于温度的长波模，出射波方程的行为几乎与经典的一样。另一方面，动力学输运描述可以在半经典粒子制度。包括波动在内，它的形式类似于现象学的玻尔兹曼-朗之万描述。然而，我们将指出与玻尔兹曼-朗之万方案相比的一些严重的差异.作为进一步的副产品，我们还注意到如何发生所谓的收缩奇点是规避了一个明确的物理必要性的阻尼内的单粒子传播。

Single-Speed Molecular Dynamics of Hard Parallel Squares and Cubes

The fluid and solid equations of state for hard parallel squares and cubes are reinvestigated here over a wide range of densities. We use a novel single-speed version of molecular dynamics. Our results are compared with those from earlier simulations, as well as with the predictions of the virial series, the cell model, and Kirkwood's many-body single-occupancy model. The single-occupancy model is applied to give the absolute entropy of the solid phases just as was done earlier for hard disks and hard spheres. The excellent agreement found here with all relevant previous work shows very clearl…