No abstract

Due to the opacity of most granular materials, it is often desirable to have three dimensional (3D) particle tracking techniques beyond optical imaging to explore granular dynamics. Using inertial measurement units (IMU) embedded in a projectile, we obtain the trajectory of projectile impacting on a granular medium under microgravity using tri-axial acceleration and angular velocity data. In addition to the standard algorithm for reconstruction, we emphasize solutions to various sources of error to determine projectile trajectory accurately.

We consider a one-dimensional Dicke lattice with complex photon hopping amplitudes and investigate the influence of time-reversal symmetry breaking due to synthetic magnetic fields. We show that, by tuning the total flux threading the loop, the universality class of superradiant phase transition (SPT) changes from that of the mean-field fully-connected systems to one that features anomalous critical phenomena. The anomalous SPT exhibits a closing of the energy gap with different critical exponents on both sides of transition and a discontinuity of correlations and fluctuation despite it being a continuous phase transition. In the anomalous normal phase, we find that a non-mean-field critical exponent for the closing energy gap and non-divergent fluctuations and correlations appear, which we attribute to the asymmetric dispersion relation. Moreover, we show that the nearest neighborhood complex hopping induces effective long-range interactions for position quadratures of the cavity fields, whose competition leads to a series of first order phase transitions among superradiant phases with varying degrees of frustration. The resulting multicritical points also show anomalous features such as two coexisting critical scalings on both sides of the transition. Our work shows that the interplay between the broken time-reversal symmetry and frustration on bosonic lattice systems can give rise to anomalous critical phenomena that have no counter part in fermionic or spin systems or time-reversal symmetric quantum optical systems.