Multipole groups and fracton phenomena on arbitrary crystalline lattices

Multipole symmetries are of interest in multiple contexts, from the study of fracton phases, to nonergodic quantum dynamics, to the exploration of new hydrodynamic universality classes. However, prior explorations have focused on continuum systems or hypercubic lattices. In this work, we systematically explore multipole symmetries on arbitrary crystal lattices. We explain how, given a crystal structure (specified by a space group and the occupied Wyckoff positions), one may systematically construct all consistent multipole groups. We focus on two-dimensional crystal structures for simplicity, although our methods are general and extend straightforwardly to three dimensions. We classify the possible multipole groups on all two-dimensional Bravais lattices, and on the kagome and breathing kagome crystal structures to illustrate the procedure on general crystal lattices. Using Wyckoff positions, we provide an in-principle classification of all possible multipole groups in any space group. We explain how, given a valid multipole group, one may construct an effective Hamiltonian and a low-energy field theory. We then explore the physical consequences, beginning by generalizing certain results originally obtained on hypercubic lattices to arbitrary crystal structures. Next, we identify two seemingly novel phenomena, including an emergent, robust subsystem symmetry on the triangular lattice, and an exact multipolar symmetry on the breathing kagome lattice that does not include conservation of charge (monopole), but instead conserves a vector charge. This makes clear that there is new physics to be found by exploring the consequences of multipolar symmetries on arbitrary lattices, and this work provides the map for the exploration thereof, as well as guiding the search for emergent multipolar symmetries and the attendant exotic phenomena in real materials based on nonhypercubic lattices.Comment: 23 pages, 9 figure

Simulator Performance vs. Neurophysiologic Monitoring: Which is More Relevant to Assess Driving Impairment?

Previously, we reported on circadian variation in driving simulator performance and neurophysiologic evidence of sleep intrusion into consciousness in a pilot study of healthy individuals. We have since expanded this “normative” sample and run a prospective comparison study with a sample of clinical patients reporting excessive daytime sleepiness (EDS) as a chief complaint. Thirty healthy adults (mean age of 31.3 ± 11.5) and 27 EDS patients (47.0 ± 13.7) with valid driver’s licenses were included. Subjects performed four intentionally soporific 30-minute driving simulations at two-hour intervals while undergoing continuous EEG monitoring for microsleep (MS) episodes. Measured variables included: subjective ratings of sleepiness and alertness prior to each drive, lane position accuracy, mean speed, speed deviation, mean reaction time (RT) to “virtual” wind gusts as well as off-road events, i.e., “crashes.” In comparing normative individuals and EDS patients, significant between-group differences were found between subjective ratings, RT, crashes and MS. Both groups showed a significant a tendency towards RT slowing during afternoon drives, with this circadian effect appearing most pronounced for EDS patients. Significant between-group differences were also found on subjective ratings of sleepiness and alertness, although diurnal fluctuation of subjective sleepiness ratings was significant only for the EDS group. Objective EEG MS monitoring demonstrated escalating sleep intrusion with repeated drives in both groups, but particularly for the EDS group. Total crash rates were three times higher in EDS patients, with an increasing trend towards crash-proneness in the late afternoon. In summary, we found significantly impaired performance on some, though not all, driving parameters for EDS patients. While increased crash rate may be the most dramatic of these, slowing of RT was the most statistically robust. EEG monitoring was able to document increased propensity towards MS episodes in patients with EDS, which we suggest is causative in creating this impairment. It remains unclear whether a neurophysiologic or simulator approach captures impairment due to sleepiness with greater sensitivity and specificity. A hybrid approach combining data from both sources may be optimal, and also could be integrated in commercial vehicle use. We suggest that the need for a more accurate hospitalbased screening tool for assessment of driving impairment due to sleep disorders remains an important issue for physicians and legislators dealing with driving competency