Rejection-free particle swap Monte Carlo simulations to efficiently explore dense packings of spheres and to solve long-standing questions on the glass transition

即使远远高于堵塞转变的堆积分数，球体的无定形堆积也处于准平衡状态，即，在行为类似平衡的状态下，但真正的平衡--可能是结晶的或大小分离的--尚未达到。准平衡对于研究玻璃系统的性质和获得可能的理想玻璃化转变有特别的兴趣，这种转变有时被推测存在于沿着准平衡路径更远的某个地方。我们希望实现一种新的模拟方法，以便有效地在填充分数处使系统达到准平衡，而这些系统目前无法进行模拟。对于我们的新方法，我们希望结合两种非常不同的成功模拟技术的基本思想。我们新方法的想法的起点是粒子交换的蒙特卡罗模拟，这种模拟最近被广泛用于探索这种极其密集的堆积。这些模拟的一个限制是为了增加密度而提出的粒子交换的拒绝数量越来越大。为了解决这个问题，我们让我们受到无拒绝事件链模拟的启发，这些模拟不服从详细平衡，但由于全球平衡仍然成立，达到平衡的速度甚至比传统的蒙特卡罗模拟更快。在我们的新方法中，我们沿着关于颗粒大小的链进行交换。最重要的是，没有粒子交换必须被拒绝。我们的初步模拟表明，我们可以在堆积分数比堆积分数大得多的情况下对系统进行热化，在那里可以用其他方法进行平衡。该项目的一个目标是实现我们对硬球和软球的有效模拟。然而，该项目的主要目标与我们可以确定的填料的物理性质有关。例如，我们对准平衡、Gardner转变或高维标度的性质感兴趣。我们想要回答的问题包括：准平衡线的终点处有过渡吗？无序准平衡态的堆积分数有上限吗？加德纳的过渡线在哪里结束？理想的玻璃化转变在不同的维度上表现如何？注意，通过我们的新方法，我们希望能够使系统准平衡，直到预测的玻璃紧密堆积分数，从而能够直接进入这个转变(如果存在的话)，以及第一次对所提到的问题的答案。

Even far above the packing fraction of the jamming transition amorphous packings of spheres occur in quasi-equilibrium states, i.e., in states that behave like equilibrium except that the true equilibrium - probably crystalline or size separated - has not been reached. The quasi-equilibrium is of special interest for the study of the properties of glassy systems and to obtain further insights of a possible ideal glass transition that sometimes is conjectured to exist somewhere further along the quasi-equilibrium pathway. We want to implement a new simulation method in order to efficiently quasi-equilibrate systems at packing fractions that at the moment are not accessible for simulations. For our new approach we want to combine the basic ideas of two very different successful simulation techniques. The starting point for our idea of a new method are Monte Carlo simulations with particle swaps that recently have been widely used to explore such extremely dense packings. One limitation of these simulations are the increasingly large rejection numbers of proposed particle swaps for increasing density. To overcome this issue, we let us inspired by rejection-free event chain simulations that do not obey detailed balance, but as global balance still holds, equilibrium is achieved that even is faster then for conventional Monte Carlo simulations. In our new approach we perform swaps along chains concerning the particle size. Most importantly, no particle swap has to be rejected. Our preliminary simulations show that we can thermalized systems at packing fraction that are much larger than the packing fractions where equilibration is possible with other methods. One goal of the project is the implementation of our efficient simulation for hard as well as for soft spheres. However, the major goals of the project are related to the physics of the packings that we can determine. For example, we are interested in the properties of the quasi-equilibrium, the Gardner transition, or the scaling in higher dimensions. Among the questions that we want to answer are: Is there a transition at the endpoint of the quasi-equilibrium line? Is there an upper limit for the packing fraction that can occur for disordered quasi-equilibrium states at all? Where does the Gardner transition line ends? And how does the ideal glass transition behave in different dimensions? Note that with our new approach we expect to be able to quasi-equilibrate systems up to the predicted glass close packing fraction thus having direct access to this transition (if it exists) as well as the answers to the mentioned questions for the first time.