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

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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.