We investigate numerically the clustering behavior of a system of phase oscillators with positive and negative couplings under a periodic external driving field with a bimodal distribution of driving phases. The phase distribution and the mean speed
of the traveling state, as well as the order parameter for synchronization, are computed as the driving amplitude is varied. We observe that the periodically-driven system can also host traveling states for parameters in the same range as those for the case of a system without a driving field. The traveling speed is found to depend non-monotonically on the driving amplitude. In particular, oscillators divide into four clusters and move in pairs. Further, depending on the driving amplitude, two kinds of traveling mode arise: pairs of clusters traveling in the same direction (symmetric mode) and in opposite directions (antisymmetric mode). In the latter case (antisymmetric traveling mode), the average phase speed of the whole system apparently vanishes. A phenomenological argument for such behavior is given.
We investigate paramagnetic metal-insulator transitions in the infinite-dimensional ionic Hubbard model at finite temperatures. By means of the dynamical mean-field theory with an impurity solver of the continuous-time quantum Monte Carlo method, we
show that an increase in the interaction strength brings about a crossover from a band insulating phase to a metallic one, followed by a first-order transition to a Mott insulating phase. The first-order transition turns into a crossover above a certain critical temperature, which becomes higher as the staggered lattice potential is increased. Further, analysis of the temperature dependence of the energy density discloses that the intermediate metallic phase is a Fermi liquid. It is also found that the metallic phase is stable against strong staggered potentials even at very low temperatures.
Starting from a master equation, we derive the evolution equation for the size distribution of elements in an evolving system, where each element can grow, divide into two, and produce new elements. We then probe general solutions of the evolution qu
ation, to obtain such skew distributions as power-law, log-normal, and Weibull distributions, depending on the growth or division and production. Specifically, repeated production of elements of uniform size leads to power-law distributions, whereas production of elements with the size distributed according to the current distribution as well as no production of new elements results in log-normal distributions. Finally, division into two, or binary fission, bears Weibull distributions. Numerical simulations are also carried out, confirming the validity of the obtained solutions.
Dynamics of a coarse-grained model for the room-temperature ionic liquid, 1-ethyl-3-methylimidazolium hexafluorophosphate, couched in the united-atom site representation are studied via molecular dynamics simulations. The dynamically heterogeneous be
havior of the model resembles that of fragile supercooled liquids. At or close to room temperature, the model ionic liquid exhibits slow dynamics, characterized by nonexponential structural relaxation and subdiffusive behavior. The structural relaxation time, closely related to the viscosity, shows a super-Arrhenius behavior. Local excitations, defined as displacement of an ion exceeding a threshold distance, are found to be mainly responsible for structural relaxation in the alternating structure of cations and anions. As the temperature is lowered, excitations become progressively more correlated. This results in the decoupling of exchange and persistence times, reflecting a violation of the Stokes-Einstein relation.
A variety of metal vacuum systems display the celebrated 1/t pressure, namely power-law dependence on time t, with the exponent close to unity, the origin of which has been a long-standing controversy. Here we propose a chemisorption model for water
adsorbates, based on the argument for fermion behaviour of water vapour adsorbed on a stainless-steel surface, and obtain analytically the power-law behaviour of pressure, with an exponent of unity. Further, the model predicts that the pressure should depend on the temperature T according to T^(3/2), which is indeed confirmed by our experiment. Our results should help elucidate the unique characteristics of the adsorbed water.
To understand the non-exponential relaxation associated with solvation dynamics in the ionic liquid 1-ethyl-3-methylimidazolium hexafluorophosphate, we study power spectra of the fluctuating Franck-Condon energy gap of a diatomic probe solute via mol
ecular dynamics simulations. Results show 1/f dependence in a wide frequency range over 2 to 3 decades, indicating distributed relaxation times. We analyze the memory function and solvation time in the framework of the generalized Langevin equation using a simple model description for the power spectrum. It is found that the crossover frequency toward the white noise plateau is directly related to the time scale for the memory function and thus the solvation time. Specifically, the low crossover frequency observed in the ionic liquid leads to a slowly-decaying tail in its memory function and long solvation time. By contrast, acetonitrile characterized by a high crossover frequency and (near) absence of 1/f behavior in its power spectra shows fast relaxation of the memory function and single-exponential decay of solvation dynamics in the long-time regime.
