We study a stationary state of a single self-propelled, athermal particle in linear and quadratic external potentials. The self-propulsion is modeled as a fluctuating force evolving according to the Ornstein-Uhlenbeck process, independently of the state of the particle. Without an external potential, in the long time limit, the self-propelled particle moving in a viscous medium performs diffusive motion, which allows one to identify an effective temperature. We show that in the presence of a linear external potential the stationary state distribution has an exponential form with the sedimentation length determined by the effective temperature of the free self-propelled particle. In the presence of a quadratic external potential the stationary state distribution has a Gaussian form. However, in general, this distribution is not determined by the effective temperature of the free self-propelled particle.

Unusual features of the vibrational density of states D(ω) of glasses allow one to rationalize their peculiar low-temperature properties. Simulational studies of D(ω) have been restricted to studying poorly annealed glasses that may not be relevant to experiments. Here we report on D(ω) of zero-temperature glasses with kinetic stabilities ranging from poorly annealed to ultrastable glasses. For all preparations, the low-frequency part of D(ω) splits between extended and quasi-localized modes. Extended modes exhibit a boson peak crossing over to Debye behavior (Dex(ω) ~ ω2) at low-frequency, with a strong correlation between the two regimes. Quasi-localized modes obey Dloc(ω) ~ ω4, irrespective of the stability. The prefactor of this quartic law decreases with increasing stability, and the corresponding modes become more localized and sparser. Our work is the first numerical observation of quasi-localized modes in a regime relevant to experiments, and it establishes a direct connection between glasses’ stability and their soft vibrational modes

We combine computer simulations and analytical theory to investigate the glassy dynamics in dense assemblies of athermal particles evolving under the sole influence of self-propulsion. Our simulations reveal that when the persistence time of the self-propulsion is increased, the local structure becomes more pronounced whereas the long-time dynamics first accelerates and then slows down. We explain these surprising findings by constructing a nonequilibrium microscopic theory which yields nontrivial predictions for the glassy dynamics. These predictions are in qualitative agreement with the simulations and reveal the importance of steady state correlations of the local velocities to the nonequilibrium dynamics of dense self-propelled particles.

The two-dimensional freezing transition is very different from its three-dimensional counterpart. In contrast, the glass transition is usually assumed to have similar characteristics in two and three dimensions. Using computer simulations, here we show that glassy dynamics in supercooled two- and three-dimensional fluids are fundamentally different. Specifically, transient localization of particles on approaching the glass transition is absent in two dimensions, whereas it is very pronounced in three dimensions. Moreover, the temperature dependence of the relaxation time of orientational correlations is decoupled from that of the translational relaxation time in two dimensions but not in three dimensions. Last, the relationships between the characteristic size of dynamically heterogeneous regions and the relaxation time are very different in two and three dimensions. These results strongly suggest that the glass transition in two dimensions is different than in three dimensions.

In a recent publication C. C. Yu and H. M. Carruzzo [Phys. Rev. E 69, 051201 (2004)] determined that the minimum sampling time to calculate the specific heat in a supercooled liquid using energy fluctuations is on the order of 10(3) alpha relaxation times, which is much longer than the sampling time used in most simulations. We demonstrate how the specific heat can be calculated from simulations run to 15 alpha relaxation times, and use statistical arguments to explain the systematic deviation of the specific heat calculated from a simulation of finite length from the true expectation value of the specific heat.