U(2,2) gravity on noncommutative space with symplectic structure

The classical Einstein's gravity can be reformulated from the constrained U(2,2) gauge theory on the ordinary (commutative) four-dimensional spacetime. Here we consider a noncommutative manifold with a symplectic structure and construct a U(2,2) gauge theory on such a manifold by using the covariant coordinate method. Then we use the Seiberg-Witten map to express noncommutative quantities in terms of their commutative counterparts up to the first-order in noncommutative parameters. After imposing constraints we obtain a noncommutative gravity theory described by the Lagrangian with up to nonvanishing first order corrections in noncommutative parameters. This result coincides with our previous one obtained for the noncommutative SL(2,C) gravity.Comment: 13 pages, no figures; v2: 14 pages, clarifications and references added; v3: 16 pages, title changed, clarifications and references added; v4: 17 pages, clarifications added, this final version accepted by Physical Review

Non-perturbative Dynamical Decoupling Control: A Spin Chain Model

This paper considers a spin chain model by numerically solving the exact model to explore the non-perturbative dynamical decoupling regime, where an important issue arises recently (J. Jing, L.-A. Wu, J. Q. You and T. Yu, arXiv:1202.5056.). Our study has revealed a few universal features of non-perturbative dynamical control irrespective of the types of environments and system-environment couplings. We have shown that, for the spin chain model, there is a threshold and a large pulse parameter region where the effective dynamical control can be implemented, in contrast to the perturbative decoupling schemes where the permissible parameters are represented by a point or converge to a very small subset in the large parameter region admitted by our non-perturbative approach. An important implication of the non-perturbative approach is its flexibility in implementing the dynamical control scheme in a experimental setup. Our findings have exhibited several interesting features of the non-perturbative regimes such as the chain-size independence, pulse strength upper-bound, noncontinuous valid parameter regions, etc. Furthermore, we find that our non-perturbative scheme is robust against randomness in model fabrication and time-dependent random noise

Maximally localized states and quantum corrections of black hole thermodynamics in the framework of a new generalized uncertainty principle

As a generalized uncertainty principle (GUP) leads to the effects of the minimal length of the order of the Planck scale and UV/IR mixing, some significant physical concepts and quantities are modified or corrected correspondingly. On the one hand, we derive the maximally localized states --- the physical states displaying the minimal length uncertainty associated with a new GUP proposed in our previous work. On the other hand, in the framework of this new GUP we calculate quantum corrections to the thermodynamic quantities of the Schwardzschild black hole, such as the Hawking temperature, the entropy, and the heat capacity, and give a remnant mass of the black hole at the end of the evaporation process. Moreover, we compare our results with that obtained in the frameworks of several other GUPs. In particular, we observe a significant difference between the situations with and without the consideration of the UV/IR mixing effect in the quantum corrections to the evaporation rate and the decay time. That is, the decay time can greatly be prolonged in the former case, which implies that the quantum correction from the UV/IR mixing effect may give rise to a radical rather than a tiny influence to the Hawking radiation.Comment: 27 pages, 10 figures, 4 tables; v2: 30 pages, sections 3-6 substantially revised but conclusions unchanged; v3: 27 pages, clarifications added; v4: 29 pages, clarifications and references added, final version to appear in Advances in High Energy Physic

Realization of Zero-Refractive-Index Lens with Ultralow Spherical Aberration

Optical complex materials offer unprecedented opportunity to engineer fundamental band dispersion which enables novel optoelectronic functionality and devices. Exploration of photonic Dirac cone at the center of momentum space has inspired an exceptional characteristic of zero-index, which is similar to zero effective mass in fermionic Dirac systems. Such all-dielectric zero-index photonic crystals provide an in-plane mechanism such that the energy of the propagating waves can be well confined along the chip direction. A straightforward example is to achieve the anomalous focusing effect without longitudinal spherical aberration, when the size of zero-index lens is large enough. Here, we designed and fabricated a prototype of zero-refractive-index lens by comprising large-area silicon nanopillar array with plane-concave profile. Near-zero refractive index was quantitatively measured near 1.55 um through anomalous focusing effect, predictable by effective medium theory. The zero-index lens was also demonstrated to perform ultralow longitudinal spherical aberration. Such IC compatible device provides a new route to integrate all-silicon zero-index materials into optical communication, sensing, and modulation, and to study fundamental physics on the emergent fields of topological photonics and valley photonics.Comment: 14 pages, 4 figure

Massive charged particle's tunneling from spherical charged black hole

We generalize the Parikh-Wilczek scheme to the tunneling of a massive charged particle from a general spherical charged black hole. We obtain that the tunneling probability depends on the energy, the mass and the charge of the particle. In particular, the modified Hawking temperature is related to the charge. Only at the leading order approximation can the standard Hawking temperature be reproduced. We take the Reissner-Nordstr\"{o}m black hole as an example to clarify our points of view, and find that the accumulation of Hawking radiation makes it approach an extreme black hole.Comment: 10 pages, no figures; v2: a minor typo corrected; v3: 11 pages, clarification and reference added, final version to be published in EPL; v4: minor modifications to match the published versio

SAM-RL: Sensing-Aware Model-Based Reinforcement Learning via Differentiable Physics-Based Simulation and Rendering

Model-based reinforcement learning (MBRL) is recognized with the potential to be significantly more sample efficient than model-free RL. How an accurate model can be developed automatically and efficiently from raw sensory inputs (such as images), especially for complex environments and tasks, is a challenging problem that hinders the broad application of MBRL in the real world. In this work, we propose a sensing-aware model-based reinforcement learning system called SAM-RL. Leveraging the differentiable physics-based simulation and rendering, SAM-RL automatically updates the model by comparing rendered images with real raw images and produces the policy efficiently. With the sensing-aware learning pipeline, SAM-RL allows a robot to select an informative viewpoint to monitor the task process. We apply our framework to real-world experiments for accomplishing three manipulation tasks: robotic assembly, tool manipulation, and deformable object manipulation. We demonstrate the effectiveness of SAM-RL via extensive experiments. Supplemental materials and videos are available on our project webpage at https://sites.google.com/view/sam-rl.Comment: Submitted to IEEE International Conference on Robotics and Automation (ICRA) 202

On the exponents of primitive, ministrong digraphs with shortest elementary circuit length s

AbstractLet MDs(n) = {D | D is a primitive ministrong digraph with n vertices, and the shortest cycle length of D is s}, and bs(n) = max{γ(D) | D ∈ MDs(n)}, where γ(D) is the primitive exponent of D. Our main results are: (1) we give explicit expressions for bs(n); (2) for s ≠ 2, 6, we give a necessary and sufficient condition for a digraph D ∈ MDs(n) with γ(D) = bs(n)