A variant of Horn's problem and derivative principle

Identifying the spectrum of the sum of two given Hermitian matrices with fixed eigenvalues is the famous Horn's problem.In this note, we investigate a variant of Horn's problem, i.e., we identify the probability density function (abbr. pdf) of the diagonals of the sum of two random Hermitian matrices with given spectra. We then use it to re-derive the pdf of the eigenvalues of the sum of two random Hermitian matrices with given eigenvalues via \emph{derivative principle}, a powerful tool used to get the exact probability distribution by reducing to the corresponding distribution of diagonal entries.We can recover Jean-Bernard Zuber's recent results on the pdf of the eigenvalues of two random Hermitian matrices with given eigenvalues. Moreover, as an illustration, we derive the analytical expressions of eigenvalues of the sum of two random Hermitian matrices from \rG\rU\rE(n) or Wishart ensemble by derivative principle, respectively.We also investigate the statistics of exponential of random matrices and connect them with Golden-Thompson inequality, and partly answer a question proposed by Forrester. Some potential applications in quantum information theory, such as uniform average quantum Jensen-Shannon divergence and average coherence of uniform mixture of two orbits,are discussed.Comment: 24 pages, LaTeX; a new result, i.e., Theorem 3.7, is added and several references are include

Research of the active reflector antenna using laser angle metrology system

Active reflector is one of the key technologies for constructing large telescopes, especially for the millimeter/sub-millimeter radio telescopes. This article introduces a new efficient laser angle metrology system for the active reflector antenna of the large radio telescopes, with a plenty of active reflector experiments mainly about the detecting precisions and the maintaining of the surface shape in real time, on the 65-meter radio telescope prototype constructed by Nanjing Institute of Astronomical Optics and Technology (NIAOT). The test results indicate that the accuracy of the surface shape segmenting and maintaining is up to micron dimension, and the time-response can be of the order of minutes. Therefore, it is proved to be workable for the sub-millimeter radio telescopes.Comment: 10 pages, 15 figure

High cycle fatigue and ratcheting interaction of laser powder bed fusion stainless steel 316L:Fracture behaviour and stress-based modelling

Variations in the physical and mechanical properties of parts made by laser power bed fusion (L-PBF) could be affected by the choice of processing or post-processing strategies. This work examined the influence of build orientation and post-processing treatments (annealing or hot isostatic pressing) on the fatigue and fracture behaviours of L-PBF stainless steel 316L in the high cycle fatigue region, i.e. 104 – 106 cycles. Experimental results show that both factors introduce significant changes in the plastic deformation properties, which affect fatigue strength via the mechanism of fatigue-ratcheting interaction. Cyclic plasticity is characterised by hardening, which promotes mean stress insensitivity and improved fatigue resistance. Fatigue activities, involving the initiation of crack at defects and microstructural heterogeneities, are of greater relevance to the longer life region where the global deformation mode is elastic. As the simultaneous actions of ratcheting and fatigue generate complex nonlinear interactions between the alternating stress amplitude and mean stress, the fatigue properties could not be effectively predicted using traditional stress-based models. A modification to the Goodman relation was proposed to account for the added effects of cyclic plasticity and was demonstrated to produce good agreement with experimental results for both cyclic hardening and softening materials.EDB (Economic Devt. Board, S’pore)Accepted versio

Unifying ultrafast demagnetization and intrinsic Gilbert damping in Co/Ni bilayers with electronic relaxation near the Fermi surface

The ability to controllably manipulate the laser-induced ultrafast magnetic dynamics is a prerequisite for future high speed spintronic devices. The optimization of devices requires the controllability of the ultrafast demagnetization time, , and intrinsic Gilbert damping, . In previous attempts to establish the relationship between and , the rare-earth doping of a permalloy film with two different demagnetization mechanism is not a suitable candidate. Here, we choose Co/Ni bilayers to investigate the relations between and by means of time-resolved magneto-optical Kerr effect (TRMOKE) via adjusting the thickness of the Ni layers, and obtain an approximately proportional relation between these two parameters. The remarkable agreement between TRMOKE experiment and the prediction of breathing Fermi-surface model confirms that a large Elliott-Yafet spin-mixing parameter is relevant to the strong spin-orbital coupling at the Co/Ni interface. More importantly, a proportional relation between and in such metallic films or heterostructures with electronic relaxation near Fermi surface suggests the local spin-flip scattering domains the mechanism of ultrafast demagnetization, otherwise the spin-current mechanism domains. It is an effective method to distinguish the dominant contributions to ultrafast magnetic quenching in metallic heterostructures by investigating both the ultrafast demagnetization time and Gilbert damping simultaneously. Our work can open a novel avenue to manipulate the magnitude and efficiency of Terahertz emission in metallic heterostructures such as the perpendicular magnetic anisotropic Ta/Pt/Co/Ni/Pt/Ta multilayers, and then it has an immediate implication of the design of high frequency spintronic devices

2-{2,6-Bis[bis(4-fluorophenyl)methyl]-4-chlorophenylimino} -3-aryliminobutylnickel(II) bromide complexes: Synthesis, characterization, and investigation of their catalytic behavior

The series of 2-{2,6-bis[di(4-fluorophenyl)methyl]-4-chlorophenylimino}-3- aryliminobutane derivatives (L1-L5) and their nickel(II) dibromide complexes (Ni1-Ni5) were synthesized, and all organic compounds were fully characterized by the Fourier transform infrared (FT-IR) and nuclear magnetic resonance (NMR) spectroscopy and by elemental analysis, while the nickel complexes were characterized by FT-IR spectroscopy, elemental analysis, as well as by single-crystal X-ray diffraction for two representative examples, namely Ni1 and Ni4. A distorted tetrahedral geometry was observed for these four-coordinate nickel complexes. Upon the activation with either Methylaluminoxane or modified methylaluminoxane as co-catalyst, all nickel complex precatalysts showed very high activity toward ethylene polymerization with activities of up to 10 7 g(PE)·mol -1 (Ni)·h -1 , and afforded highly branched polyethylene with a bimodal distribution. © 2014 Elsevier B.V