Breakdown Of Agreement Research Articles

Microscopic ergodicity breaking governs the emergence and evolution of elasticity in glass-forming nanoclay suspensions.

We report a study combining x-ray photon correlation spectroscopy (XPCS) with in situ rheology to investigate the microscopic dynamics and mechanical properties of aqueous suspensions of the synthetic hectorite clay Laponite, which is composed of charged, nanometer-scale, disk-shaped particles. The suspensions, with particle concentrations ranging from 3.25 to 3.75 wt%, evolve over time from a fluid to a soft glass that displays aging behavior. The XPCS measurements characterize the localization of the particles during the formation and aging of the soft-glass state. The fraction of localized particles, f_{0}, increases rapidly during the early formation stage and grows more slowly during subsequent aging, while the characteristic localization length r_{loc} steadily decreases. Despite the strongly varying rates of aging at different concentrations, both f_{0} and r_{loc} scale with the elastic shear modulus G^{'} in a manner independent of concentration. During the later aging stage, the scaling between r_{loc} and G^{'} agrees quantitatively with a prediction of naive mode coupling theory. Breakdown of agreement with the theory during the early formation stage indicates the prevalence of dynamic heterogeneity, suggesting the soft solid forms through precursors of dynamically localized clusters.

Breakdown of agreement between non-relativistic and relativistic quantum dynamical predictions in the non-relativistic regime

To study quantum dynamics in the non-relativistic regime, the standard practice is to use non-relativistic quantum mechanics, instead of the relativistic theory, because it is thought the approximate non-relativistic result is always close to the relativistic one. Here we present a theoretical argument that this expectation is not true in general. In addition, supporting numerical evidence for the free rotor and hydrogen atom also shows the agreement between the two theories can break down quickly. For the radial Rydberg wave packet in hydrogen atom, the breakdown can occur before spontaneous emission and thus could be tested experimentally. Our surprising result shows relativistic quantum mechanics must be used, instead of the approximate non-relativistic theory, to correctly study quantum dynamics in the non-relativistic regime after the breakdown time. This paradigm shift opens a new avenue of research in a wide range of fields from atomic to molecular, chemical and condensed-matter physics.

Statistical Predictions for the Dynamics of a Low-Speed System: Newtonian versus Special-Relativistic Mechanics

The Newtonian and special-relativistic statistical predictions for the mean, standard deviation and probability density function of the position and momentum are compared for the periodically-delta-kicked particle at low speed. Contrary to expectation, we find that the statistical predictions, which are calculated from the same parameters and initial Gaussian ensemble of trajectories, do not always agree if the initial ensemble is sufficiently well-localized in phase space. Moreover, the breakdown of agreement is very fast if the trajectories in the ensemble are chaotic, but very slow if the trajectories in the ensemble are non-chaotic. The breakdown of agreement implies that special-relativistic mechanics must be used, instead of the standard practice of using Newtonian mechanics, to correctly calculate the statistical predictions for the dynamics of a low-speed system.

Comparison of Newtonian and Special-Relativistic Trajectories with the General-Relativistic Trajectory for a Low-Speed Weak-Gravity System

We show, contrary to expectation, that the trajectory predicted by general-relativistic mechanics for a low-speed weak-gravity system is not always well-approximated by the trajectories predicted by special-relativistic and Newtonian mechanics for the same parameters and initial conditions. If the system is dissipative, the breakdown of agreement occurs for chaotic trajectories only. If the system is non-dissipative, the breakdown of agreement occurs for chaotic trajectories and non-chaotic trajectories. The agreement breaks down slowly for non-chaotic trajectories but rapidly for chaotic trajectories. When the predictions are different, general-relativistic mechanics must therefore be used, instead of special-relativistic mechanics (Newtonian mechanics), to correctly study the dynamics of a weak-gravity system (a low-speed weak-gravity system).

Newtonian and special-relativistic predictions for the trajectories of a low-speed scattering system

Newtonian and special-relativistic predictions, based on the same model parameters and initial conditions for the trajectory of a low-speed scattering system are compared. When the scattering is chaotic, the two predictions for the trajectory can rapidly diverge completely, not only quantitatively but also qualitatively, due to an exponentially growing separation taking place in the scattering region. In contrast, when the scattering is nonchaotic, the breakdown of agreement between predictions takes a very long time, since the difference between the predictions grows only linearly. More importantly, in the case of low-speed chaotic scattering, the rapid loss of agreement between the Newtonian and special-relativistic trajectory predictions implies that special-relativistic mechanics must be used, instead of the standard practice of using Newtonian mechanics, to correctly describe the scattering dynamics.