论文标题
均匀加热的颗粒气中的线性响应
Linear response in the uniformly heated granular gas
论文作者
论文摘要
我们分析了均匀加热的颗粒气的线性响应特性。随机驾驶的强度固定了系统达到的非平衡稳态中颗粒温度的值。在这里，我们研究了两种具体情况。首先，我们调查了单个驾驶强度的跳跃后，系统的``直接''放松。这项研究是通过两种不同的方法进行的。我们不仅可以在稳态周围线性性地线性化方程，还可以为相关响应函数得出广义的不平衡波动 - 散落关系。其次，我们在一个更复杂的实验中研究了系统的行为，特别是类似Kovacs的协议，并在驾驶中有两次跳跃。根据直接松弛函数的特性来解释异常的科瓦奇响应的出现：这是第二种模式以非弹性性的临界值更改符号，它使异常行为与正常行为划分。将分析结果与动力学方程的数值模拟进行了比较，并找到了良好的一致性。
We analyse the linear response properties of the uniformly heated granular gas. The intensity of the stochastic driving fixes the value of the granular temperature in the non-equilibrium steady state reached by the system. Here, we investigate two specific situations. First, we look into the ``direct'' relaxation of the system after a single (small) jump of the driving intensity. This study is carried out by two different methods. Not only do we linearise the evolution equations around the steady state, but also derive generalised out-of-equilibrium fluctuation-dissipation relations for the relevant response functions. Second, we investigate the behaviour of the system in a more complex experiment, specifically a Kovacs-like protocol with two jumps in the driving. The emergence of anomalous Kovacs response is explained in terms of the properties of the direct relaxation function: it is the second mode changing sign at the critical value of the inelasticity that demarcates anomalous from normal behaviour. The analytical results are compared with numerical simulations of the kinetic equation, and a good agreement is found.
