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1. chinaXiv:201708.00168 [pdf]

Exact Solution of the Generalized Rabi Model

Degang Zhang
分类: 物理学 >> 普通物理:统计和量子力学,量子信息等

The generalized Rabi model is exactly solved by employing the unitary transformation method in the occupation number representation. The analytical expressions for the complete energy spectrum consisting of two sub-energy spectra are presented in the whole range of all the physical parameters. Each energy level possesses twofold degeneracy and is determined by the parameter in the unitary transformation, which obeys a highly nonlinear equation. The corresponding eigenfunction is a convergent infinite series in terms of these physical parameters. Due to the level crossings between the neighboring eigenstates at certain parameter values, such the degeneracies could lead to novel physical phenomena in these quantum systems with the light-matter interaction.

提交时间: 2017-10-18 点击量59, 下载量42

2. chinaXiv:201710.00002 [pdf]

在液滴作用下悬浮薄膜的毛细皱纹标度律

孙博华
分类: 物理学 >> 电磁学、光学、声学、传热、经典力学和流体动力学

研究意义: 悬浮于液体的薄膜在其上有个液滴(drop),由于液滴的表面张力的作用,薄膜会发生皱纹。皱纹的长度和数量对于测量和标定薄膜材料的性能非常有意义。 J. Huang, M. Juszkiewicz, W. H. de Jeu, E. Cerda, T.Emrick, N. Menon and T. P. Russell在 Science, 317, 650(2007) 通过细致的实验,并通过曲线拟合得到了薄膜皱纹长度和数量的经验表达式,2010年D. Vella, M. Adda-Bedia and E. Cerda, Soft Matter 6,5778 (2010),利用圆形薄板理论进行了解析和数值分析,从理论上部分地验证了 Huang et al(2007)的经验公式。 存在的问题是: 1. 目前得到的经验表达式是否是普遍适用的结果? 2.如果不是普遍适用,那么在什么情况下可以使用这些经验公式? 3.目前的结果都是在各向同性薄膜的情况下获得的结果,那么对于正交各向同性薄膜的情况如何把现有表达式推广到正交各向同性薄膜? 4.Huang (2007), Vella (2010)和其他成果都是只是研究静态情况,而实际情况是,表面张力的作用是一个动力学的过程,随着时间的发展,皱纹长度和数量要发生变化,如何在静态成果的基础上,推广到皱纹动力学? 5.另外,液滴的半径如果超过毛细尺度,重力就起主导作用,就必须考虑重力的影响(之前的论文都没有考虑),这时的皱纹长度和数量与时间的关系满足什么标度律? 本文的工作: 首先我们使用量纲分析方法,推导出皱纹长度和数量的一般关系,发现皱纹长度和数量由二个组合无量纲参数的联合作用控制,在一般非线性变形的情况下,没有普遍适用的规律(标度律),只有在线性小变形的情况,才有普遍适用的标度律。 在小变形的情况下,皱纹长度主要有薄膜面内刚度与表面张力之比控制,其物理意义就是,在液滴薄膜张力一定的情况下,薄膜面内拉伸性能越好皱纹越长,反之,越短。皱纹数量取决于液滴的半径和薄膜弯曲刚度与表面张力之比,薄膜越容易弯曲皱纹越多,反之,越少。这里的结果完全符合物理观察。 对于小变形情况,我们把各向同性薄膜的情况推广到正交各向同性的情况。 对于皱纹动力学问题,我们利用Tanner的液滴半径随时间的标度律,结合我们得到的结果,成功地得到了皱纹长度和数量的动力学结果。以前没有看到皱纹动力学的结果。 最后,我们给出了重力主导的皱纹长度和数量的表达式,发现在重力主导的情况下,皱纹长度和数量对于给定的问题,是一个常数。以前没有看到重力主导情况下的皱纹结果。

提交时间: 2017-09-30 点击量324, 下载量56

3. chinaXiv:201709.00179 [pdf]

论毛细动力学的解

Bohua Sun
分类: 物理学 >> 普通物理:统计和量子力学,量子信息等

毛细动力学方程的求解可以说是个百年经典难题,由于它是一个非线性微分方程,以前只有分段近似解析估计,从来没有适用于全时间域的精确解和近似解析解,本文给出了二种解(精确级数解和近似解析解),由于精确级数解收敛慢,本文提出了一个近似解析解,这个近似解析解统一并改进了以前一切近似估计,并与目前的有关数值计算和实验都非常吻合。 总体上说,毛细动力学过程是表面张力与壁阻力和重力联合作用的相互斗争并达到统一的结果。开始阶段表面张力起主导作用,后来壁阻力和重力起主导作用。整个动力学过程基本可以这样来定性描述:在一个无限大的蓄水池中,在初始状态,毛细的高度和速度都是零。由于表面张力的作用,液体获得了启动的初始加速度(初始加速度绝不能为零!),开始以一个比较均匀的速度上升,在上升阶段表面张力起主导作用;但是,随着毛细的上升,壁摩阻和重力开始起作用,企图阻止毛细的上升,它们的联合作用在一个时间点成功地使毛细上升减速,当毛细上升到达 H 高度后,会在 H  附近振动非常短的时间,然后衰减直至停留在 H 高度。至此。表面张力与壁阻力、重力达到对立统一,毛细动力学过程结束,一切归于平静。

提交时间: 2017-09-29 点击量560, 下载量189

4. chinaXiv:201709.00123 [pdf]

Inflationary Attractor in Braneworld Scenario

Zong-Kuan Guo; Hong-Sheng Zhang; Yuan-Zhong Zhang
分类: 物理学 >> 普通物理:统计和量子力学,量子信息等

We demonstrate the attractor behavior of inflation driven by a scalar field or a tachyon field in the context of recently proposed four-dimensional effective gravity induced on the world-volume of a three-brane in five-dimensional Einstein gravity, and we obtain a set of exact inflationary solutions.Phase portraits indicate that an initial kinetic term decays rapidly and it does not prevent the onset of inflation. The trajectories more rapidly reach the slow rolling curve in braneworld scenario than in the standard cosmology.

提交时间: 2017-09-27 点击量266, 下载量65

5. chinaXiv:201709.00124 [pdf]

Inflection point inflation and dark energy in supergravity

Tie-Jun Gao; Zong-Kuan Guo
分类: 物理学 >> 普通物理:统计和量子力学,量子信息等

We consider an inflection point inflationary model in supergravity with a single chiral superfield and show that the predicted values of the scalar spectral index and tensor-to-scalar ratio are consistent with the Planck 2015 results. In this model supersymmetry is strongly broken after inflation, which results in a non-SUSY de-Sitter vacuum responsible for the recent accelerated expansion of the Universe.

提交时间: 2017-09-27 点击量261, 下载量57

6. chinaXiv:201709.00125 [pdf]

Black Holes in the Dilatonic Einstein-Gauss-Bonnet Theory in Various Dimensions II– Asymptotically AdS Topological Black Holes –

Zong-Kuan GUO; Nobuyoshi Ohta; Takashi Torii
分类: 物理学 >> 普通物理:统计和量子力学,量子信息等

We study asymptotically AdS topological black hole solutions with k = 0 (plane symmetric) in the Einstein gravity with Gauss-Bonnet term, the dilaton and a “cosmo-logical constant” in various dimensions. We derive the field equations for suitable ansatz for general D dimensions. We determine the parameter regions including dilaton cou-plings where such solutions exist and construct black hole solutions of various masses numerically in D = 4, 5, 6 and 10 dimensional spacetime with (D − 2)-dimensional hypersurface of zero curvature.

提交时间: 2017-09-27 点击量282, 下载量68

7. chinaXiv:201709.00126 [pdf]

Accelerating Cosmologies in theEinstein-Gauss-Bonnet Theory with Dilaton

Kazuharu BAMBA; Zong-Kuan Guo; Nobuyoshi Ohta
分类: 物理学 >> 普通物理:统计和量子力学,量子信息等

We study cosmological solutions in the low-energy effective heterotic string theory, which is the Einstein gravity with Gauss-Bonnet term and the dilaton. We show that the field equations are cast into an autonomous system for flat internal and external spaces, and derive all the fixed points in the system. We also examine the time evolution of the solutions and whether the solutions can give (transient) accelerated expansion of our four-dimensional space in the Einstein frame.

提交时间: 2017-09-27 点击量177, 下载量29

8. chinaXiv:201709.00127 [pdf]

Probing the Coupling between Dark Components of the Universe

Zong-Kuan Guo; Nobuyoshi Ohta; Shinji Tsujikawa
分类: 物理学 >> 普通物理:统计和量子力学,量子信息等

We place observational constraints on a coupling between dark energy and dark matter by using 71 Type Ia supernovae (SNe Ia) from the first year of the five-year Supernova Legacy Survey (SNLS), the cosmic microwave background (CMB) shift parameter from the three-year Wilkinson Microwave Anisotropy Probe (WMAP), and the baryon acoustic oscillation (BAO) peak found in the Sloan Digital Sky Survey (SDSS). The interactions we study are (i) constant coupling #14; and (ii) varying coupling #14;(z) that depends on a redshift z, both of which have simple parametrizations of the Hubble parameter to confront with observational data. We find that the combination of the three databases marginalized over a present dark energy density gives stringent constraints on the coupling,−0.08 < #14; < 0.03 (95% CL) in the constant coupling model and −0.4 < #14;0 < 0.1 (95% CL) in the varying coupling model, where #14;0 is a present value. The uncoupled #3;CDM model (wX = −1 and #14; = 0) still remains a good fit to the data, but the negative coupling (#14; < 0) with the equation of state of dark energy wX < −1 is slightly favoured over the #3;CDM model.

提交时间: 2017-09-27 点击量244, 下载量28

9. chinaXiv:201709.00128 [pdf]

Realizing Scale-invariant Density Perturbations in Low-energy Effective String Theory

Zong-Kuan Guo; Nobuyoshi Ohta; Shinji Tsujikawa
分类: 物理学 >> 普通物理:统计和量子力学,量子信息等

We discuss the realization of inflation and resulting cosmological perturbations in the low-energy effective string theory. In order to obtain nearly scale-invariant spectra of density perturbations and a suppressed tensor-to-scalar ratio, it is generally necessary that the dilaton field #30; is effectively decoupled from gravity together with the existence of a slowly varying dilaton potential. We also study the effect of second-order corrections to the tree-level action which are the sum of a Gauss-Bonnet term coupled to #30; and a kinetic term (∇#30;)4. We find that it is possible to realize observationally supported spectra of scalar and tensor perturbations provided that the correction is dominated by the (∇#30;)4 term even in the absence of the dilaton potential. When the Gauss-Bonnet term is dominant, tensor perturbations exhibit violent negative instabilities on small-scales about a de Sitter background in spite of the fact that scale-invariant scalar perturbations can be achieved.

提交时间: 2017-09-27 点击量214, 下载量57

10. chinaXiv:201709.00129 [pdf]

Two-Field Quintom Models in the w − w Plane

Zong-Kuan Guo; Yun-Song Piao; Xinmin Zhang; Yuan-Zhong Zhang
分类: 物理学 >> 普通物理:统计和量子力学,量子信息等

The w−w′ plane, defined by the equation of state parameter for the dark energy and its derivative with respect to the logarithm of the scale factor, is useful to the study of classifying the dynamical dark energy models. In this note, we examine the evolving behavior of the two-field quintom models with w crossing the w = −1 barrier in the w − w′ plane. We find that these models can be divided into two categories, type A quintom in which w changes from > −1 to < −1 and type B quintom in which w changes from < −1 to > −1 as the universe expands.

提交时间: 2017-09-27 点击量817, 下载量493

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