Very Old Isolated Compact Objects as Dark Matter Probes

Very old isolated neutron stars and white dwarfs have been suggested to be probes of dark matter. To play such a role, two requests should be fulfilled, i.e., the annihilation luminosity of the captured dark matter particles is above the thermal emission of the cooling compact objects (request-I) and also dominate over the energy output due to the accretion of normal matter onto the compact objects (request-II). Request-I calls for very dense dark matter medium and the critical density sensitively depends on the residual surface temperature of the very old compact objects. The accretion of interstellar/intracluster medium onto the compact objects is governed by the physical properties of the medium and by the magnetization and rotation of the stars and may outshine the signal of dark matter annihilation. Only in a few specific scenarios both requests are satisfied and the compact objects are dark matter burners. The observational challenges are discussed and a possible way to identify the dark matter burners is outlined.Comment: 9 pages including 1 Figure, to appear in Phys. Rev.

On the Optimal Batch Size for Byzantine-Robust Distributed Learning

Byzantine-robust distributed learning (BRDL), in which computing devices are likely to behave abnormally due to accidental failures or malicious attacks, has recently become a hot research topic. However, even in the independent and identically distributed (i.i.d.) case, existing BRDL methods will suffer from a significant drop on model accuracy due to the large variance of stochastic gradients. Increasing batch sizes is a simple yet effective way to reduce the variance. However, when the total number of gradient computation is fixed, a too-large batch size will lead to a too-small iteration number (update number), which may also degrade the model accuracy. In view of this challenge, we mainly study the optimal batch size when the total number of gradient computation is fixed in this work. In particular, we theoretically and empirically show that when the total number of gradient computation is fixed, the optimal batch size in BRDL increases with the fraction of Byzantine workers. Therefore, compared to the case without attacks, the batch size should be set larger when under Byzantine attacks. However, for existing BRDL methods, large batch sizes will lead to a drop on model accuracy, even if there is no Byzantine attack. To deal with this problem, we propose a novel BRDL method, called Byzantine-robust stochastic gradient descent with normalized momentum (ByzSGDnm), which can alleviate the drop on model accuracy in large-batch cases. Moreover, we theoretically prove the convergence of ByzSGDnm for general non-convex cases under Byzantine attacks. Empirical results show that ByzSGDnm has a comparable performance to existing BRDL methods under bit-flipping failure, but can outperform existing BRDL methods under deliberately crafted attacks

Extracting the Quantum Geometric Tensor of an Optical Raman Lattice by Bloch State Tomography

In Hilbert space, the geometry of the quantum state is identified by the quantum geometric tensor (QGT), whose imaginary part is the Berry curvature and real part is the quantum metric tensor. Here, we propose and experimentally implement a complete Bloch state tomography to directly measure eigenfunction of an optical Raman lattice for ultracold atoms. Through the measured eigenfunction, the distribution of the complete QGT in the Brillouin zone is reconstructed, with which the topological invariants are extracted by the Berry curvature and the distances of quantum states in momentum space are measured by the quantum metric tensor. Further, we experimentally test a predicted inequality between the Berry curvature and quantum metric tensor, which reveals a deep connection between topology and geometry