Electron capture of iron group nuclei in magnetars

Using the theory of relativity in superstrong magnetic fields (SMFs) and nuclear shell model, we carry out estimation for electron capture (EC) rates on iron group nuclei in SMFs. The rates of change of electronic abundance (RCEA) due to EC are also investigated in SMFs. It is concluded that the EC rates of most iron group nuclides are increased greatly by SMFs and even exceeded by nine orders of magnitude. On the other hand, RCEA is influenced greatly by SMFs and even reduced by more than eight orders of magnitude in the EC reaction.We also compare our results with those of Fuller et al.(FFN) and Aufderheide et al.(AUFD) in the case with and without SMFs. The results show that our results are in good agreement with AUFD's, but the rates of FFN's are about close to one order of magnitude bigger than ours in the case without SMFs. On the contrary, our calculated rates for most nuclides in SMFs are increased and even exceeded as much as for nine and eight orders of magnitude of compared to FFN's and AUFD's results, which is in the case without SMFs, respectively.Comment: 8 pages, 13 figures, accepted by MNRA

Electron capture of strongly screening nuclides 56^{56}Fe, 56^{56}Co, 56^{56}Ni , 56^{56}Mn ,56^{56}Cr and 56^{56}V in presupernova

According to the Shell-Model Monte Carlo method, basing on the Random Phase Approximation and the linear response theory, we carried out an estimation on electron capture of strongly screening nuclides $^{56}$Fe, $^{56}$Co, $^{56}$Ni , $^{56}$Mn ,$^{56}$Cr and $^{56}$V in strong electron screening (SES)in presupernova. The EC rates are decreased greatly and even exceed $21.5\%$ in SES. We also compare our results with those of Aufderheide (AFUD), which calculated by the method of Aufderheide in SES. Our results are agreed reasonably well with AUFD at higher density-temperature surroundings (e.g. $\rho_7>60, T_9=15.40$) and the maximum error is $\sim$0.5$\%$. However, the maximum error is $\sim$13.0$\%$ at lower density surroundings (e.g. $^{56}$Cr at $\rho_7=10, T_9=15.40, Y_e=0.41$ ). On the other hand, we also compared our results in SES with those of FFN's and Nabi's, which is in the case without SES. The comparisons show that our results are lower more than one order magnitude than FFN's, but about $7.23\%$ than Nabi's.Comment: 6 pages,5 figures, MNRAS, Volume 433, Issue 2, p.1108-111

Strong screening effects on resonant nuclear reaction 23^{23}Mg (p,γ)(p,\gamma) 24^{24}Al in the surface of magnetars

Based on the theory of relativistic superstrong magnetic fields(SMFs), by using the method of the Thomas-Fermi-Dirac approximations, we investigate the problem of strong electron screening(SES) in SMFs, and the influence of SES on the nuclear reaction of $^{23}$Mg $(p, \gamma)$$^{24}$Al. Our calculations show that the nuclear reaction will be markedly effected by the SES in SMFs in the surface of magnetars. Our calculated screening rates can increase two orders of magnitude due to SES in SMFs

Supernova {\beta}^- decay of nuclides 53Fe, 54Fe, 55Fe, and 56Fe in strongly screened plasma

The electron screening strong effect on the electron energy and threshold energy of the beta decay reaction. in this paper, we study the $\beta^-$ decay rates of some iron isotopes. The electron screening beta decay rates increase by about two orders of magnitude. The strong screening beta decay rates due to Q-value correction are by more than one order of magnitude higher than those of without Q-value correction.Comment: 10 pages, 45 figures, accepted for publication in Resarch in Astronomy and Astrophysic

Simultaneous approximation on affine subspaces

We solve the convergence case of the generalized Baker-Schmidt problem for simultaneous approximation on affine subspaces, under natural diophantine type conditions. In one of our theorems, we do not require monotonicity on the approximation function. In order to prove these results, we establish asymptotic formulae for the number of rational points close to an affine subspace. One key ingredient is a sharp upper bound on a certain sum of reciprocals of fractional parts associated with the matrix defining the affine subspace.Comment: To appear in IMR

Phase matching condition for enhancement of phase sensitivity in quantum metrology

We find a phase matching condition for enhancement of sensitivity in a Mach-Zehnder interferometer illuminated by an arbitrary state in one input port and an odd(even) state in the other port. Under this condition, the Fisher information becomes maximal with respect to the relative phase of two modes and the phase sensitivity is enhanced. For the case with photon losses, we further find that the phase matching condition keeps unchanged with a coherent state and a coherent superposition state as the input states.Comment: 4 pages, 2 figure

Benchmark Tests of Convolutional Neural Network and Graph Convolutional Network on HorovodRunner Enabled Spark Clusters

The freedom of fast iterations of distributed deep learning tasks is crucial for smaller companies to gain competitive advantages and market shares from big tech giants. HorovodRunner brings this process to relatively accessible spark clusters. There have been, however, no benchmark tests on HorovodRunner per se, nor specifically graph convolutional network (GCN, hereafter), and very limited scalability benchmark tests on Horovod, the predecessor requiring custom built GPU clusters. For the first time, we show that Databricks' HorovodRunner achieves significant lift in scaling efficiency for the convolutional neural network (CNN, hereafter) based tasks on both GPU and CPU clusters, but not the original GCN task. We also implemented the Rectified Adam optimizer for the first time in HorovodRunner.Comment: AAAI 2020 W8 Deep Learning on Graphs: Methodologies and Applications Accepted Poster Number 2

A new insight into neutrino energy loss by electron capture of iron group nuclei in magnetars surface

Based on the relativistic mean-field effective interactions theory, and Lai dong model \citep{b37, b38, b39}, we discuss the influences of superstrong magnetic fields (SMFs) on electron Fermi energy, nuclear blinding energy, and single-particle level structure in magnetars surface. By using the method of Shell-Model Monte Carlo (SMMC), and the Random Phase Approximation (RPA) theory, we detailed analyze the neutrino energy loss rates(NELRs) by electron capture (EC) for iron group nuclei in SMFs.Comment: 22 pages, 8 figures, accepted for publication in ApJS. arXiv admin note: text overlap with arXiv:astro-ph/0606674, arXiv:nucl-th/9707052, arXiv:nucl-th/9801012, arXiv:1505.07304 by other author

Quantum Fisher Information of Entangled Coherent States in a Lossy Mach-Zehnder Interferometer

We give an analytical result for the quantum Fisher information of entangled coherent States in a lossy Mach-Zehnder Interferometer recently proposed by J. Joo et al. [Phys. Rev. Lett. 107, 083601(2011)]. For small loss of photons, we find that the entangled coherent state can surpass the Heisenberg limit. Furthermore, The formalism developed here is applicable to the study of phase sensitivity of multipartite entangled coherent states.Comment: 14 pages, 1 figur

Quantum Fisher information and symmetric logarithmic derivative via anti-commutators

Symmetric logarithmic derivative (SLD) is a key quantity to obtain quantum Fisher information (QFI) and to construct the corresponding optimal measurements. Here we develop a method to calculate the SLD and QFI via anti-commutators. This method is originated from the Lyapunov representation and would be very useful for cases that the anti-commutators among the state and its partial derivative exhibits periodic properties. As an application, we discuss a class of states, whose squares linearly depend on the states themselves, and give the corresponding analytical expressions of SLD and QFI. A noisy scenario of this class of states is also considered and discussed. Finally, we readily apply the method to the block-diagonal states and the multi-parameter estimation problems.Comment: 12 pages, no figur