分层介质的正交波函数

一、问题的提出 讨论声波在浅海中传播时,常采用下列介质模型:海面被看成为绝对软边界,海水为分层不均匀介质,其中密度为常数ρ_1,声速是深度的函数c_1(z),海底被看为均匀液体半空间,其密度与声速分别为ρ_2与c_2(见图1)。本文采用物理量Ψ来描述声场,它与声压P及质点振动速度V的关系为: P=ρ~(1/2)Ψ,V=1/(iωρ~(1/2))gradΨ,此处ω是声波的圆频率,ρ是介质的密度。对于图1所示的分层介质,Ψ应满足波动方程     

Equilibrium dynamics of the sub-Ohmic spin-boson model under bias

Using the bosonic numerical renormalization group method, we studied the equilibrium dynamical correlation function C(ω) of the spin operator σ_z for the biased sub-Ohmic spin-boson model. The small-ω behavior C(ω) ∝ω~s is found to be universal and independent of the bias ε and the coupling strength α(except at the quantum critical point α = αc and ε = 0). Our NRG data also show C(ω) ∝χ~2ω~s for a wide range of parameters, including the biased strong coupling regime(ε = 0 and α α_c), supporting the general validity of the Shiba relation. Close to the quantum critical point αc,the dependence of C(ω) on α and ε is understood in terms of the competition between ε and the crossover energy scale ω_0~*of the unbiased case. C(ω) is stable with respect to ε for ε《ε~*. For ε》ε~*, it is suppressed by ε in the low frequency regime. We establish that ε~*∝(ω_0~*)~(1/θ)holds for all sub-Ohmic regime 0≤s 1, with θ = 2/(3s) for 0 s≤1/2 and θ = 2/(1 + s) for 1/2 s 1. The variation of C(ω) with α and ε is summarized into a crossover phase diagram on the α–ε plane.     

厚度与应变效应对La0.67Ca0.33MnO3薄膜电输运与居里温度的影响

在厚度为25—400nm范围内，系统地研究了 (001)SrTiO_3(STO), (001)LaAlO_3(LAO)衬底上La_0.67Ca_0.33Mn_O.3 (LCMO)薄膜的电输运与居里温度T_C随薄膜厚度及衬底的变化. 结果表明，随薄膜变薄，电阻率ρ增加，T_C降低. 对于同一薄膜厚度，LCMO/STO薄膜的ρ大于LCMO/LAO基上的薄膜的ρ. T_C衬底的依赖关系则与ρ相反. 分析表明，LCMO薄膜的低温区电阻温度(ρ-T) 符合关系式ρ=ρ_0+Bω_s/sin h^2(ω_s/2/k_BT)+CT^n， 其中ρ_0为剩余电阻；等号右端第二项反映软光学模声子对电子散射的贡献；第三项包括其余可能散射机 理在电输运过程中所起的作用；B，ωs（软光学模声子的平均频率）与C都为拟合系数. 高温区的电输运则由小极化子跃迁模型ρ=DT×exp（E_a/k_BT）描述（E_a为极化子激 发能）. 根据ρ_0，ωs，E_a以及T_Ｃ变化，初步讨论了薄膜中的厚度与应变效应. 进一步 研究发现ωs，E_a的变化与T_C相关，从而说明极化子效应为影响T_C变化的主要因素. 关键词： 锰氧化物薄膜 电输运 居里温度 极化子     

厚度与应变效应对La0.67 Ca0.33 MnO3薄膜电输运与居里温度的影响

在厚度为25-400nm范围内,系统地研究了(001)SrTiO3(STO),(001)LaAlO3(LAO)衬底上La0.67Ca0.33MnO3(LCMO)薄膜的电输运与居里温度TC随薄膜厚度及衬底的变化.结果表明,随薄膜变薄,电阻率ρ增加,TC降低.对于同一薄膜厚度,LCMO/STO薄膜的ρ大于LCMO/LAO基上的薄膜的ρ.TC与衬底的依赖关系则与ρ相反.分析表明,LCMO薄膜的低温区电阻温度(ρ-T)符合关系式ρ=ρ0+Bωs/sinh2(hωs/2/kBT)+CTn,其中ρ0为剩余电阻;等号右端第二项反映软光学模声子对电子散射的贡献;第三项包括其余可能散射机理在电输运过程中所起的作用;B,ωs(软光学模声子的平均频率)与C都为拟合系数.高温区的电输运则由小极化子跃迁模型ρ=DT×exp(Ea/kBT)描述(Ea为极化子激发能).根据ρ0,ωs,Ea以及TC变化,初步讨论了薄膜中的厚度与应变效应.进一步研究发现ωs,Ea的变化与TC相关,从而说明极化子效应为影响TC变化的主要因素.     

Variation of dielectronic satellite intensity factors with n for dielectronic recombination processes in selected lithium—like ions

Satellite intensity factors F^*₂(s→f) have been calculated for the 1s²2s+εl→(1s²3l′nl″)^*→1s²2sml''+hν dielectronic recombination processes of lithium-like V, Cu, Se, Ag and Ba ions. The relevant atomic parameters have been calculated explicitly for all intermediate resonance states |s〉≡|1s²3l′nl″SLJ〉 with n=3－9 in the intermediate coupling scheme. The 1/n³ scaling, which has often been used in extrapolating F^*(s→f) for n≥4, is tested against these values of F^*₂(s→f).     

电子在超短激光脉冲修正场中的动力学特性研究

给出了一种精确描述超短、紧聚焦激光脉冲的新方法，其思路是根据两个无量纲小量ε=1/(ω0t0)和s=1/(k0w0)（其中ω0=ck0为中心振荡频率，t0为脉冲延迟时间，w0为激光束腰半径）进行展开来计算脉冲的高阶修正场.在激光束近轴近似表达式的基础上，给出了高斯脉冲一阶修正场的解析表达式，并研究发现其振幅和相位相对于零阶修正场（即长脉冲近似）的修正量都在ε的量级甚至更小.另外对电子在超短高斯脉冲一阶修正场中的动力学特性研究发现：对于ω0t0>20的情况，零阶修正场可以正确地描述电子被光场加速的特性；当ω0t0<20时，则需要采用高阶修正场. 关键词： 超短激光脉冲 激光加速     

关于向量介子的辐射衰变

1.近年来已发现了(不稳定的)向量介子(V)的八重态 (ρ~+,ρ~-,ρ~0,K~*+,K ~*0,K ~*0,ω~0) (1)它们衰变到赝标量介子(S)及光子的各种辐射衰变振幅是其中向量介子V的极化向量是e~V,赝标量介子S的动量是P,光子γ的动量是q,极化向量是e~γ。衰变宽度是本文中我们采用方h=C=m_n的单位系统。 2.Okubo由么正对称模型得出上述各种振幅间的关系式由此不难得出各种耦合常数间的关系式:我们只需由某种方法定出其中一个耦合常数,例如gp~0π~0r,即可得出(3)式中的各种宽度。 3.现在来考虑衰变     

关于一级近似T_c级数解的收敛问题

本文通过一个实例说明:μ~* =0时,一级近似T_c级数解的收敛半径既不是由z_(ph)=-integral from n=0 to (ω_(ph)) (dωg(ω)·ω＇/ω_(ph)~2-ω~2),也不是由z_(ph)=integral from n=0 to (ω_(ph)) (dωg(ω)ω~2/ω_(ph)~2 ω~2)决定的。     

单参数喇叭中的一个共轭关系

在单参数喇叭中各声学量只和一个坐标x有关.记声压为Pe~(jωt),媒质质点的振速为Ue~(jωt),媒质的静态密度为ρ,煤质中声速为c,圆频率为ω,喇叭横截面半径为R,它的倒数为K.分别引入表征声压和振速特性的参量:Π=RP,U=ρcRu,由此得喇叭声阻抗率和ρc的比值为     

超音速绕流Mach-Zehnder干涉图分析的Abel变换

本文处理了含激波的柱对称或球对称抛射体超音速统流Mach-Zehnder干涉图分析的Abel变换问题。我们对一般的Abel积分方程研究了具有有限个间断点的解的某些性质;将其应用到Mach-Zehnder干涉图的干涉条纹移动δ(x)和密度ρ(x)间的Abel变换上,得到了三个有明显物理意义的结论,(1)干涉图上的任一直线上的干涉条纹移动δ(x)是x的连续函数;(2)若在截面1-1上的圆环r=c处有激波,则当x→c_时,δ’(x)～L/(c-x)~(1/2);(3)若除尖点c外,干涉条纹移动δ(x)是光滑的,limδ’(x)存在,且当x→c_时,δ’(x)～L/(c-x)~(1/2),则流场中于圆环r=c处出现激波,在激波两侧密度跳跃值为Δρ=λ*L/K(2c)~(1/2),且对r≥c和r相似文献   

■_(u,d,s)~*→ D_(u,d,s)~*V(V = D_(d,s)~(*-), K~(*-), ρ~-) weak decays

Motivated by the rapid development of heavy flavor physics experiments, we study the tree-dominated nonleptonic ■_(u,d,s)~*→ D_(u,d,s)~*V(V = D_(d,s)~(*-), K~(*-), ρ~-) decays within the factorization approach. The relevant transition form factors are calculated by employing the covariant light-front quark model. Helicity amplitudes are calculated and analyzed in detail, and a very clear hierarchical structure |H-0| ≈ 2|H00| |H0-| ≈ |H| |H0+| ≈ |H++| is presented.The branching fractions are computed and discussed. Numerically, the CKM-favored ■*q→ D_q~*ρ~-and D_q~*D_s~(*-) decays have relatively large branching fractions, ■O(10~(-8)), and could be observed by LHC and Belle-II experiments in the future.     

Branching ratio and CP asymmetry of Bs→K0(1430)η(') decays in the PQCD approach

In the two-quark model supposition for K0*(1430), which can be viewed as either the first excited state (ScenarioⅠ) or the lowest lying state (Scenario Ⅱ), the branching ratios and the direct CP-violating asymmetries for decays s0 → K0*0(1430)η (’) are studied by employing the perturbative QCD factorization approach. We find the following results: (a) The CP averaged branching ratios ofs0 → K0*0 (1430)η ands0→ K0*0(1430)η’ are small and both in the order of 10-7 . If one views K0* (1430) as the lowest lying state, B(s0→K0*0(1430)η) ≈ 3.9×10-7 and B(s0→K0*0(1430)η’) ≈ 7.8×10-7.(b) While the direct CP-violating asymmetries of these two decays are not small: if we still take the parameters of K0* (1430) in scenario , ACPdir(s0→K0*0(1430)η) ≈ 56.2% and ACPdir(s0→ K0*0(1430)η’) ≈ 42.4%. (c) The annihilation contributions will play an important role in accounting for future data, because both the branching ratios and the direct CP asymmetries of these two decays are sensitive to the annihilation type contributions.     

类锂离子(Z=3～100)磁偶和电偶的跃迁几率和能级间隔的相对论计算

采用全相对论多组态Dirac-Fock方法，分别计算了类锂离子（Z＝3－100)的磁偶跃迁1s^23s^2S1/2→1s^22s^2S1/2和电偶跃迁1s^2p^2P1/2→1s^22s^2S1/2的能级间隔，QED贡献和跃迁几率，比较了两者的参数与核电荷数Z的关系的差异，认为原子序数很大时，磁偶跃迁几率不能忽视。     

Pu_3体系的结构与势能函数

用相对论有效原子实势 (RECP)和密度泛函 (B3LYP)方法对Pun(n =2 ,3)体系的结构进行了优化 ,得到了Pu2 和Pu3分子的几何构型分别为D∞h,D3h,其基态分别为 13和 19重态 .在B3LYP RECP水平上得到Pu2 分子的光谱常数ωe=5 2 .3845cm- 1 ,ωe 　χe=0 .0 2 0 1cm- 1 和Pu3分子的谐振频率 (ν1 =5 6 .90 0 7cm- 1 ,ν2 =5 7.1816cm- 1 ,ν3=6 4 0 785cm- 1 )等性质 ,并通过正规方程组和多体展式理论 ,得到了Pu2 ,Pu3的分析势能函数 .     

全国部分地区非物理类专业大学生物理竞赛题解第十六届非物理类专业大学生物理竞赛试题及解答

一、填空题 (共 54分 )1 . (4分 )由空中垂直下落的物体所受空气阻力 f与空气的密度ρ、物体的有效横截面积 S、下落的速率 v的平方成正比 ,阻力的大小可表示为 f=CρSv2 ,其中 C为阻力系数 ,一般在 0 .2～ 0 .5之间 ,ρ= 1 .2 kg/m3 ,物体下落经过一段时间将达匀速 ,这称为终极速率 .试估算质量为 80 kg、有效横截面为0 .6m2的某人从高空跳下 ,他下落的终极速率v终 = km/hr(千米 /小时 ) .解 :当 f =mg时 ,v终 =mgCρS=80× 9.80 .3× 1 .2× 0 .6= 60 .2 m/s=2 1 6km/hr式中 C取 0 .3.2 . (5分 )有一半球形光滑的碗 ,小球 I在碗的球心…     

ρ-ω mixing in J/ψ→VP decays

The study of ρ-ω mixing has mainly focused on vector meson decays with isospin I = 1, namely theρ(ω)→π+π- process. In this paper, we present a study of ρ-ω mixing in ρ(ω)→π+π-π0(I = 0) using a flavor parameterization model for the J/ψ→VP process. By fitting a theoretical framework to PDG data, we obtain the SU(3)-breaking effect parameters sV = 0.03±0.12, sP = 0.17±0.17 and the ρ-ω mixing polarization operatorΠρω =(0.006±0.011) GeV2. New values are found for the branching ratios when the mixing effect is incorporated:Br(J/ψ→ωπ0)=(3.64±0.37)×10-4, Br(J/ψ→ωη)=(1.48±0.17)×10-3, Br(J/ψ→ωη)=(1.55±0.56)×10-4, these are different from the corresponding PDG2012 values by 19%, 15% and 15%, respectively.     

The Role of α_1(1260) in π~-p→α_1~-(1260)p and π~-p → π~-ρ~0p Reactions Near Threshold

We report on a theoretical study of the π~-ρ→α1(1260)p and π~-ρ→π~-ρ~0p reactions near threshold within an effective Lagrangian approach.The production process is described by t-channel ρ~0 meson exchange.For the π~-ρ→π~- ρ~0p reaction,the final π~-ρ~0 results from the decay of the α1(1260) resonance,which is assumed as a dynamically generated state from the K* K and ρπ coupled channel interactions.We calculate the total cross section of the π~-ρ→α1(1260)p reaction.It is shown that,with the coupling constant of the α1(1260) to ρπ channel obtained from the chiral unitary theory and a cut off parameter Δρ~1.5 GeV in the form factors,the experimental measurement can be reproduced.Furthermore,the total and differential cross sections of π~p→α1(1260)p→π~ρ~0p reaction are evaluated,and it is expected that our model calculations can be tested by future experiments.These reactions are important for the study of the α1(1260) resonance and would provide further constraints on the properties of the α1(1260) state.     

寻找1+－奇特态再探

为了便于BES(北京谱仪)做数据分析,本文给出了在J/ψ→ωX,ω→2π或3π,X→KKπ反应中寻找1^+－奇特态的一些新的关系式.并且对于在三级二体衰变过程J/ψ→ωX,ω→2π或3π,X→K*K,K*→Kπ中如何寻找1^+－奇特态的问题作了讨论.     

s=4.03GeV下τ±→π+π－π±υτ衰变的测量

利用北京谱仪(BES)在4.03GeV正负电子对撞能量下获取的数据,[研究了,τ+τ-产生过程.借助双标记方法分析了τ±→π+π-π±υτ衰变事例.测定分支比Br(τ±→a1±υτ→ρ0π±υτ,ρ0→π+π-=(7.3±0.5)%,Br(τ±→K*±υτ→Ks0π±υτ,Ks0→π+π-)=(0.6±1.5)×10-3.并由Daliz投影分布的分析,确认a1的主要衰变方式ρπ.同时,也观察到a1衰变中以S波贡献为主的现象.采用Kuhn模型拟合实验数据,得到:ma1=1.24±0.02GeV,Γa1T=0.57±0.07GeV.     

关于一级近似Tc级数解的收敛问题

本文通过一个实例说明:μ^*=0时,一级近似T_c级数解的收敛半径既不是由z_ph=-∫₀^(ω_ph)dωg(ω)dω·ω²/(ω_ph²-ω²),也不是由z_ph=∫₀^(ω_ph)dωg(ω)dω·ω^{2< 关键词：}