《从零学相对论》连载

正§9.2虫洞9.2.1史瓦西虫洞再次观察图9-6.在"线轴"上半部分选定某个圆周(其实是球面,其r值比2M略大),例如Q点所在的圆周,则"线轴"的下半部分必有一个r值相同的圆周,介于这两个圆周之间的"线轴"部分就称为一个虫洞(wormhole),这两个球面则称为两个洞口(mouth).洞口的选法有一定的任意性[你也可选r值比rQ略大(或小)的圆周为洞口],所以"洞口"的     

有关临界阻尼振动特性的两点证明

对于一个有阻尼的弹簧振子,振动物体的运动微分方程为式中m为振动物体的质量,K为弹簧的劲度系数,r为阻尼系数. 令(ω0为振子固有频率),=2β(β为阻尼因子),则运动微分方程变为上式的解有三种情形: A.当β2>ω01时,有过阻尼振动解 B.当β2=ω02时、有临界阻尼振动解 C.当β2<ω02时,有阻尼振动解 一、对x临(t)“临界性”的证明 当β→ω0时,从表面上看x过(t)和x阻(t)的临界形式似乎是C’1e-ω0t,为什么在x临(t)中会出现c’zte-“。‘项,对这个问题,我们作如下证明. ,设振动的初始条件X一回。,可以定出三种解中的常数,即得 Zgi() 证明1当B…     

磁性超导体的临界温度理论

本文将文献[1]中的理论推广到磁性超导体的情形,研究了自旋涨落对超导临界温度的抑制作用,给出了磁性超导体的临界温度的级数展开公式为其中系数b_0、b_4、b~2…仅仅是库仑赝势μ和电子-自旋涨落耦合常数λ_s的函数.〈ω~(2n)〉、(ω~(2n))分别为有效声子谱α~2F(ω)和有效自旋涨落谱略α_m~2F(ω)的偶次矩.本文同时还给出了上述公式与数值解的比较的数字结果,并求出电声子耦合强度的临界值为μ与λ_s之和.     

再谈科里奥利力

一、引言 讨论科里奥利力(译者注:以下简称科氏力)效应的典型例子之一是地面抛体由于地球的自转而引起的编斜。多数教科书都是忽略地球自转角速度(ω=7.27 × 10-5/秒)中线性项以上的项而得出这个问题的解。所以假定g是常数。对于适当的高度,这个假定是合理的。离心项ω×(ω×r)同g相联系,所以假定在运动中也不变化。这两个因素可以包括在运动微分方程的逐步展开之中,Pars就是这样做的。但是,正如Pars所指出的那样,空气阻力的效应远远超过在运动中由于g不是恒定的或者由于忽略了ω2项而造成的扰动。所以,在研究一般科氏抛体问题时,如果能…     

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.     

Brans-Dicke理论中的非Accetta真空虫洞解

给出与Ａｃｃｅｔｔａ等人所得到的完全不同的Ｂｒａｕｓ－Ｄｉｃｋｅ（B－Ｄ）理论真空虫洞解，且表明这类虫洞与所得到的其他虫洞不同，其喉的尺度是随着Ｅｕｃｌｉｄｅａｎ宇宙时间的增大而线性增大。     

Brans—Dicke理论中的非Accetta真空虫洞解

给出与Ａｃｃｅｔｔａ等人所得到的完全不同的Ｂｒａｕｓ－Ｄｉｃｋｅ（B－Ｄ）理论真空虫洞解，且表明这类虫洞与所得到的其他虫洞不同，其喉的尺度是随着Ｅｕｃｌｉｄｅａｎ宇宙时间的增大而线性增大。     

N2同位素分子X1∑g+态的光谱常数与分子常数

利用内收缩多参考组态相互作用方法争核价相关一致极化基aug-cc-pCV5Z在0.04-0.54 nm的核间距范围内计算了N2分子X1∑g+态的势能曲线.利用这一势能曲线并在同位素质量识别的基础上,拟合出了同位素分子14N2(X1∑g+),15N2(X1∑g+)和14N15N(X1∑g+)的光谱常数(D0,De,Re,ωe,ωexe,αe和Be)和无转动时的振动能级G(υ)、惯性转动常数Bυ和离心畸变常数Dυ等分子常数.这些结果与已有的实验值十分一致.     

BeF~+离子电子态的光谱常数研究

采用从头计算方法(Ab)研究BeF~+离子的光谱性质.在icMRCI+Q/Q5+CV+DK的理论水平下计算得到了BeF~+离子的16个态的势能曲线,为了提高精确度,对势能曲线进行核价相关修正及相对论修正两种修正计算,画出了16个态的势能曲线图.拟合势能曲线得到其光谱常数(D_e,T_e,R_e,ω_e,ω_ex_e,ω_ey_e,B_e,α_e和β_e).分别计算了各个振动态对应的的振动能级.     

BeF~+离子电子态的光谱常数研究

采用从头计算方法(Ab)研究BeF~+离子的光谱性质.在icMRCI+Q/Q5+CV+DK的理论水平下计算得到了BeF~+离子的16个态的势能曲线,为了提高精确度,对势能曲线进行核价相关修正及相对论修正两种修正计算,画出了16个态的势能曲线图.拟合势能曲线得到其光谱常数(D_e,T_e,R_e,ω_e,ω_ex_e,ω_ey_e,B_e,α_e和β_e).分别计算了各个振动态对应的的振动能级.     

New Agegraphic Dark Energy in Brans-Dicke Theory

In this paper, we investigate the new agegraphic dark energy model in the framework of Brans-Dicke theory, which is a natural extension of the Einstein's general relativity. In this framework the form of the new agegraphic dark energy density takes as ρ_q =3n² φ(t) η^-2, where η is the conformalage of the universe and φ(t) is the Brans-Dicke scalar field representing the inverse of the time-variable Newton's constant. We derive the equation of state of the new agegraphic dark energy and the deceleration parameter of the universe in the Brans-Dicke theory. It is very interesting to find that in the Brans-Dicke theory the agegraphic dark energy realizes quintom-like behavior,i.e., its equation of state crosses the phantom divide w=-1 duringthe evolution. We also compare the situation of the agegraphic darkenergy model in the Brans-Dicke theory with that in the Einstein'stheory. In addition, we discuss the new agegraphic dark energy modelwith interaction in the framework of the Brans-Dicke theory.     

Coupling of Brans-Dicke scalar field with Horava-Lifshitz gravity

We look for a Brans-Dicke type generalization of Horava-Lifshitz gravity. It is shown that such a generalization is possible within the detailed balance condition. Classically, the resulting theory reduces in the low energy limit to the usual Brans-Dicke theory with a negative cosmological constant for certain values of parameters. We then consider homogeneous, isotropic cosmology and study the effects of the new terms appearing in the model.     

Inflationary solutions in general scalar tensor theory of gravitation

Extended inflation solution in Brans-Dicke theory given by Mathiazhagan and Johri (MJ) is shown as the unique solution only if the scale factor is assumed to be a power function of the scalar field. Only the consistent solution amongst the set of solutions given by Patra, Roy and Ray is found identical to the MJ solution. Both exponential inflation and power function inflation are studied in general scalar tensor theory where the parameter to is a function of the scalar, field. It is noted that exponential inflation is forbidden in Brans-Dicke theory wherew is a constant.     

On static spherically symmetric solutions of the vacuum Brans-Dicke theory

It is shown that among the four classes of the static spherically symmetric solutions of the vacuum Brans-Dicke theory of gravity only two are really independent. Further, by matching exterior and interior (due to physically reasonable spherically symmetric matter source) scalar fields it is found that only the Brans class I solution with a certain restriction on the solution parameters may represent an exterior metric for a nonsingular massive object. The physical viability of the black hole nature of the solution is investigated. It is concluded that no physical black hole solution different from the Schwarzschild black hole is available in the Brans-Dicke theory.     

Brans-Dicke引力理论的弱场近似

Brans-Dicke引力理论是重要的修正引力理论之一,其对于研究星体运动、宇宙演化以及解释宇宙现象等起着重要的作用.寻找Brans-Dicke引力理论场方程的解对于Brans-Dicke引力理论的研究和发展具有重要意义.但由于Brans-Dicke引力理论场方程本身的高度非线性性,使得一般情况下精确求解非常困难,特殊情况下也只能求得部分精确解.幸运的是大多数情况下引力场比较弱,且在低速的条件下求场方程的近似解相对容易.本文基于弱场低速条件,详细地求解了Brans-Dicke引力理论的弱场低速近似解.首先基于弱场条件,将标量场和度规写为一阶微扰展开的形式;然后将标量场和度规代入相应的场方程得到相应的线性场方程,通过选取特定的规范条件进一步简化线性场方程;最后求解出简化的线性场方程的低速近似解.本文的求解方法可以为Brans-Dicke引力理论的教学和研究提供有益的参考.     

Large numbers hypothesis and Whitrow-Randall-Sciama relation in Brans-Dicke theory

It has recently been suggested in Brans-Dicke theory that the so-called Whitrow-Randall-Sciama relation plus the assumption of a constant deceleration parameter implies the large numbers hypothesis. It is shown that this claim is not always true.     

Escape of photons from an infinite cylinder in Brans-Dicke theory of gravitation

Solutions for a cylindrically symmetric static gravitational field in Brans-Dicke theory are obtained. It is found that the condition for escape of photons emitted from the surface of the source depends on two parameters, instead of only the mass parameter as in the case of Mardar's solution in Einstein's theory.     

Cylindrically symmetric Brans-Dicke fields. I

A class of rigorous solutions for the Brans-Dicke scalar-tensor theory for Einstein-Rosen nonstatic cylindrically symmetric metric is obtained when only scalar field is present (vacuum solutions of Brans-Dicke theory). As the solutions of Brans-Dicke vacuum fields are conformal to either zero-mass scalar field or vacuum solutions of Einstein's gravitational theory, a set of solutions conformal to the above which correspond to zero-mass scalar field has also been obtained.     

The Effect of Spatial Curvature in Scalar-Tensor Theory

We investigate the effect of the spatial curvature in extra six dimensions of ten dimensional scalar-tensor theory. As a scalar-tensor theory both string theory effective action and Brans-Dicke type action are considered. For Brans-Dicke type action with positive spatial curvature (k=1) we obtain accelerating expansion of the spacetime for specific value of the Brans-Dicke parameter ω. The value, however, is negative and far from the present universe which requires big number.     

Wormholes in vacuum Brans-Dicke theory

We present a Euclidean wormhole solution in vacuum Brans-Dicke theory, which is different from that obtained by Accetta et al. This wormhole appears to have the feature that its throat dimension increases linearly with Euclidean cosmic time, although this increase may not be measurable. It also requires a negative Brans-Dicke parameter.