Random matrix theory for transition strength densities in finite quantum systems: Results from embedded unitary ensembles

Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless fermion (or boson) systems, with say m$m$ fermions (or bosons) in N$N$ single particle states and interacting via k$k$-body interactions, we have EGUE(k$k$) [embedded GUE of k$k$-body interactions] with GUE embedding and the embedding algebra is U(N)$U\left(N\right)$. A finite quantum system, induced by a transition operator, makes transitions from its states to the states of the same system or to those of another system. Examples are electromagnetic transitions (then the initial and final systems are same), nuclear beta and double beta decay (then the initial and final systems are different), particle addition to or removal from a given system and so on. Towards developing a complete statistical theory for transition strength densities (transition strengths multiplied by the density of states at the initial and final energies), we have derived formulas for the lower order bivariate moments of the strength densities generated by a variety of transition operators. Firstly, for a spinless fermion system, using EGUE(k$k$) representation for a Hamiltonian that is k$k$-body and an independent EGUE(t$t$) representation for a transition operator that is t$t$-body and employing the embedding U(N)$U\left(N\right)$ algebra, finite-N$N$ formulas for moments up to order four are derived, for the first time, for the transition strength densities. Secondly, formulas for the moments up to order four are also derived for systems with two types of spinless fermions and a transition operator similar to beta decay and neutrinoless beta decay operators. In addition, moments formulas are also derived for a transition operator that removes k₀$k_0$ number of particles from a system of m$m$ spinless fermions. In the dilute limit, these formulas are shown to reduce to those for the EGOE version derived using the asymptotic limit theory of Mon and French (1975). Numerical results obtained using the exact formulas for two-body (k=2$k=2$) Hamiltonians (in some examples for k=3$k=3$ and 4$4$) and the asymptotic formulas clearly establish that in general the smoothed (with respect to energy) form of the bivariate transition strength densities take bivariate Gaussian form for isolated finite quantum systems. Extensions of these results to bosonic systems and EGUE ensembles with further symmetries are discussed.     

Complex turing patterns in non-linearly coupled systems

Recently pattern formation in layered structures, showing complicated superimposed patterns, has been modeled by coupling two Turing systems linearly, i.e., passively, such that the characteristic length scales of the independent systems are well separated. Here we propose a model of two non-linearly coupled Turing systems to study pattern formation in layered membrane-like structures, where the coupling plays an active role and changes the kinetics of the uncoupled systems. Extensive numerical simulations show that non-linear coupling generates a number of new regular patterns different from the ones observed earlier with linearly coupled systems. Some of them turn out to be superimposed patterns with different length scales, but many are not. Also, contrary to the linear coupling case, the strength of the non-linear coupling is found to play an important role in the formation and selection of patterns.     

Periodic solutions for a class of superquadratic Hamiltonian systems

We prove the existence of nontrivial critical points for a class of superquadratic nonautonomous second-order Hamiltonian systems by applying condition ^∗(C) to critical point theory, and some new solvability conditions of nontrivial periodic solutions are obtained.     

LD泵浦Nd:YAG/LBO蓝光激光器的低噪声运转

观察了LD泵浦Nd:YAG晶体,I类临界相位匹配LBO晶体腔内倍频的473nm蓝光激光器的噪声特性,指出蓝光噪声主要来自于不同纵模的相互耦合,并用双折射滤光片技术实现了全固态蓝光激光器的低噪声稳定运转在1.3W的泵浦功率下,获得了58mW的蓝光低噪声稳定输出.     

LD端面泵浦Nd:YAG/BIBO单模蓝光激光器

从理论上分析了准三能级系统946 nmNd:YAG全固态激光器运转的条件,并比较了几种不同的倍频晶体的特性,给出内腔倍频获得473 nm蓝光发射的方案。用波长808 nm、输出功率为2.2 W的半导体激光器泵浦Nd:YAG,采用内腔倍频的方法,在一定的温度下,用Ⅰ类临界相位匹配B IBO晶体倍频获得了473 nm 26.5 mW的单模连续蓝色激光输出,功率波动小于±5%。     

2.41 W compact efficient CW blue light generation by intra-cavity frequency doubling of a compact Nd:YAG laser

We report on a laser diode end-pumped Nd:YAG blue laser using a three-mirror-folded cavity. Three different crystals cut for type-I critical phase matching are used for the intra-cavity frequency doubling of the laser: 10-mm-long LiB₃O₅ (LBO), 15-mm-long LBO, and 10-mm-long BiB₃O₆ (BIBO). Up to 2.41 W of continuous wave output power in the blue spectral range at 473 nm is achieved with BIBO crystal (1.89 W with LBO) at the incident pump power of 16 W, the light-to-light conversion efficiency is about 15.1%.     

Synthesis and characterization of the dodecanuclear heterobimetallic Mo—Cu—S cage cluster: (Ph4P)2[{Mo2Cu2O2S2(S2)2}3(μ6-S)]

The complex (Ph₄P)₂[Mo₂S₂O₂(S₂)(S₄)] reacts with CuBr to give the dodecanuclear heterobimetallic Mo—Cu—S cage cluster: (Ph₄P)₂[{Mo₂Cu₂O₂S₂(S₂)₂}₃(473q752tr63/xxlarge956.gif" alt="mgr" align="MIDDLE" BORDER="0">₆-S)] (1), which crystallizes in the triclinic space group P1¯, a = 14.445(5), b = 15.396(5), c = 18.858(5) Å, 473q752tr63/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0"> = 103.12(3), 473q752tr63/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0"> = 101.93(2), 473q752tr63/xxlarge947.gif" alt="gamma" align="MIDDLE" BORDER="0"> = 113.92(3)°, and V = 3517(2) ų for Z = 2. The anion 1 can be described as a cage with S^2– at the center binding to six Cu atoms; the cage has two big windows each composed of a puckered Cu₃S₆ 9-membered ring.