Synthetic gauge fields enable high-order topology on Brillouin real projective plane

The topology of the Brillouin zone, foundational in topological physics, is always assumed to be a torus. We theoretically report the construction of Brillouin real projective plane ($\mathrm{RP}^2$) and the appearance of quadrupole insulating phase, which are enabled by momentum-space nonsymmorphic symmetries stemming from $\mathbb{Z}_2$ synthetic gauge fields. We show that the momentum-space nonsymmorphic symmetries quantize bulk polarization and Wannier-sector polarization nonlocally across different momenta, resulting in quantized corner charges and an isotropic binary bulk quadrupole phase diagram, where the phase transition is triggered by a bulk energy gap closing. Under open boundary conditions, the nontrivial bulk quadrupole phase manifests either trivial or nontrivial edge polarization, resulting from the violation of momentum-space nonsymmorphic symmetries under lattice termination. We present a concrete design for the $\mathrm{RP}^2$ quadrupole insulator based on acoustic resonator arrays and discuss its feasibility in optics, mechanics, and electrical circuits. Our results show that deforming the Brillouin manifold creates opportunities for realizing high-order band topology.Comment: 5 pages,5 figure

Physical essence of propagable fractional-strength optical vortices in free space

Fractional-order vector vortex beams are recently demonstrated to be new carriers of fractional-strength optical vortices. However, why can those new vortex beams formed by the combination of both unstable states propagate stably in free space? Here, we solve this scientific problem by revealing the physical essence of propagable fractional-strength optical vortices in free space.Three new understandings regarding those peculiar vortex beams are therefore proposed, namely Abbe diffraction limit, phase evolution of vortex beam, and phase binary time vector property.For the first one, owing to Abbe diffraction limit, the inherent polarization modes are intertwined together, thereby maintaining the entire peculiar vortex beams in free space. For the second one, we demonstrate the phase evolution of vortex beam, which is the physical reason of polarization rotation of fractional-order VVBs. For the third one, the phase is not merely a scalar attribute of light beam, but manifests a binary time vector property. This work provides entirely different physical viewpoints on the phase of vortex beam and Abbe diffraction limit, which may deepen our knowledge on the behavior of light beam in classical optics

Characterising User Transfer Amid Industrial Resource Variation: A Bayesian Nonparametric Approach

In a multitude of industrial fields, a key objective entails optimising resource management whilst satisfying user requirements. Resource management by industrial practitioners can result in a passive transfer of user loads across resource providers, a phenomenon whose accurate characterisation is both challenging and crucial. This research reveals the existence of user clusters, which capture macro-level user transfer patterns amid resource variation. We then propose CLUSTER, an interpretable hierarchical Bayesian nonparametric model capable of automating cluster identification, and thereby predicting user transfer in response to resource variation. Furthermore, CLUSTER facilitates uncertainty quantification for further reliable decision-making. Our method enables privacy protection by functioning independently of personally identifiable information. Experiments with simulated and real-world data from the communications industry reveal a pronounced alignment between prediction results and empirical observations across a spectrum of resource management scenarios. This research establishes a solid groundwork for advancing resource management strategy development