Conformal transformations in cosmology of modified gravity: the covariant approach perspective

The 1+3 covariant approach and the covariant gauge-invariant approach to perturbations are used to analyze in depth conformal transformations in cosmology. Such techniques allow us to obtain insights on the physical meaning of these transformations when applied to non-standard gravity. The results obtained lead to a number of general conclusions on the change of some key quantities describing any two conformally related cosmological models. For example, even if some of the geometrical properties of the cosmology are preserved (homogeneous and isotropic Universes are mapped into homogeneous and isotropic universes), it can happen that decelerating cosmologies can be mapped into accelerated ones. From the point of view of the cosmological perturbations it is shown how these fluctuation transform. We find that first-order vector and tensor perturbations equations are left unchanged in their structure by the conformal transformation, but this cannot be said of the scalar perturbations, which present differences in their evolutionary features. The results obtained are then explicitly interpreted and verified with the help of some clarifying examples based on f(R)-gravity cosmologies.     

Gravitational Waves and the Conformal Transformation

We study the problem of the behaviour of cosmological gravitational waves under conformal transformations. In spite of the apparent triviality of this question, the informations we can obtain from gravitational waves in the so-called Einstein's and Jordan's frame are not the same, mainly with respect to the choice of the initial conditions and of graviton production. The only exception seems to occur in string cosmology due to the duality properties.     

Hawking radiation from the charged and magnetized BTZ black hole via covariant anomaly

This paper discusses Hawking radiation from the charged and magnetized Ba?ados--Teitelboim--Zanelli (BTZ) black hole from the viewpoint of anomaly, initiated by Robinson and Wilczek recently. It reconstructs the electromagnetic field tensor and the Lagrangian of the field corresponding to the source with electric and magnetic charges to redefine an equivalent charge and gauge potential. It employs the covariant anomaly cancellation method to determine the compensating fluxes of charge flow and energy-momentum tensor, which are shown to match with those of the 2-dimensional blackbody radiation at the Hawking temperature exactly.     

The development of perturbations in the universe described by the nonstationary equation of state

The growth of the perturbation density in a baryon substance due to a nonstationary character of the equation of state of nonbaryon matter in the Universe is studied. It is shown that the perturbations evolve slower than within the Friedmann cosmological model. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 61–67, March, 2009.     

Nonsingular cosmological models: the massive scalar field case

The nonminimal coupling of a massive self-interacting scalar field with a gravitational field is studied. Spontaneous symmetry breaking occurs in the open universe even when the sign on the mass term is positive. In contrast to grand unified theories, symmetry breakdown is more important for the early universe and it is restored only in the limit of an infinite expansion. Symmetry breakdown is shown to occur in flat and closed universes when the mass term carries a wrong sign. The model has a naturally defined effective gravitational coupling coefficient which is rendered time-dependent due to the novel symmetry breakdown. It changes sign below a critical value of the cosmic scale factor indicating the onset of a repulsive field. The presence of the mass term severely alters the behaviour of ordinary matter and radiation in the early universe. The total energy density becomes negative in a certain domain. These features make possible a nonsingular cosmological model for an open universe. The model is also free from the horizon and the flatness problems.     

Hawking radiation from the dilaton-（anti） de Sitter black hole via covariant anomaly

Adopting the anomaly cancellation method, initiated by Robinson and Wilczek recently, this paper discusses Hawking radiation from the dilaton--(anti) de Sitter black hole. To save the underlying gauge and general covariance, it introduces covariant fluxes of gauge and energy--momentum tensor to cancel the gauge and gravitational anomalies. The result shows that the introduced compensating fluxes are equivalent to those of a 2-dimensional blackbody radiation at Hawking temperature with appropriate chemical potential.     

Physics beyond the standard model and cosmological connections: A summary from LCWS06

The international linear collider (ILC) is likely to provide us important insights into physics sector that may supersede our current paradigm, viz., the standard model. In anticipation of the possibility that the ILC may come up in the middle of the next decade, several groups are vigourously investigating its potential to explore this new sector of physics. The Linear Collider Workshop in Bangalore (LCWS06) had several presentations of such studies which looked at supersymmetry, extra dimensions and other exotic possibilities which the ILC may help us discover or understand. Some papers also looked at the understanding of cosmology that may emerge from studies at the ILC. This paper summarises these presentations.      

关于分离变量法的一个注记

从B-cklund变换出发，利用Cole-Hopf变换，一些有重要物理意义的(2+1)维非线性演化方程(组)被简化为具有两个分别关于(x,t),(y,t)的任意函数的单个线性偏微分方程.通过对该方程解的研究，获得了原方程一些新的精确解.其中，一些近年来被广泛研究的由分离变量法所获得的解也被重新得到. 关键词： B-cklund变换 Cole-Hopf变换 分离变量法 精确解     

Conformal invariance and perturbations in the two-dimensional Ising model: Surface defects

The influence of homogeneous surface perturbations on the surface critical behavior of the two-dimensional Ising model is studied through finite-size scaling and conformal invariance. Quantum chains of up to 2000 spins are studied in the fermionic version of the model. The results are deduced from the numerical solution of an eigenvalue equation for the excitation spectrum and show that conformal invariance still works for irrelevant surface perturbations.     

Collision-induced rovibrational energy transfer in small polyatomic molecules: the role of intramolecular perturbations

ABSTRACT

Various forms of time-resolved optical double-resonance spectroscopy facilitate rotationally resolved measurements of collision-induced intramolecular vibration-to-vibration (V–V) energy-transfer processes, which take a gas-phase polyatomic molecule from one distinct rovibrational energy level to another. Of longstanding mechanistic interest are questions concerning the extent to which such V–V energy transfer (ET) may be influenced by intramolecular perturbations – notably Fermi resonance (and other anharmonic mixing effects) and Coriolis coupling – within polyatomic molecular rovibrational manifolds of interest. It is evident that quantum-mechanical interference effects can arise, either inhibiting or enhancing the probability of collision-induced ET in perturbed rovibrational manifolds of certain small gas-phase polyatomic molecules, notably CO₂, D₂CO and C₂H₂. This article focuses on a blend of high-resolution rovibrational spectroscopy (characterising initial and final molecular levels and their intramolecular perturbations) and collision dynamics (with colliding molecules defined in terms of isolated-molecule spectroscopic basis states). It aims to offer fresh insights and to consider some apparent mechanistic anomalies (e.g. collision-induced quasi-continuous background effects in the 4ν_CH rovibrational manifold of C₂H₂). Various reported experiments and related theoretical treatments are critically re-examined, in order to pose and address mechanistic questions some of which still challenge detailed understanding.     

Lie algebraic approach of a charged particle in presence of a constant magnetic field via the quadratic invariant

In this paper we consider the problem of a charged harmonic oscillator under the influence of a constant magnetic field. The system is assumed to be isotropic and the magnetic field is applied along the z-axis. The canonical transformation is invoked to remove the interaction term and the system is reduced to a model containing the second harmonic generation. Two classes of the real and complex quadratic invariants (constants of motion) are obtained. We have employed the Lie algebraic technique to find the most general solution for the wave function for both real and complex invariants. Some discussions related to the advantage of using the quadratic invariants to solve the Cauchy problem instead of the direct use of the Hamiltonian itself are also given.     

Multi-soliton solutions for the three types of nonlocal Hirota equations via Riemann–Hilbert approach

The purpose of the paper is to formulate multi-soliton solutions for the nonlocal Hirota equations via the Riemann–Hilbert (RH) approach. The RH problems are constructed and the zero structures are studied via performing spectral analysis of the Lax pair. Then we consider three types of nonlocal Hirota equations by discussing different symmetry reductions of the potential matrix. On the basis of the resulting matrix RH problem under the restriction of the reflectionless case, we successfully obtain the multi-soliton solutions of the nonlocal Hirota equations.     

分数维方法研究GaAs薄膜中的极化子

本文采用分数维方法, 在讨论Al_0.3Ga_0.7As衬底上GaAs薄膜的分数维基础上, 计算了GaAs薄膜中的极化子结合能和有效质量. 随着薄膜厚度的增加, 极化子结合能和质量变化单调地减小. 当薄膜厚度L_w<70 Å并且衬底厚度L_b<200 Å时, 衬底厚度的变化对薄膜中极化子的结合能和质量变化的影响比较显著, 随着衬底厚度的增加, 薄膜中极化子的结合能和质量变化逐渐变大; 当薄膜厚度L_w>70 Å或者衬底厚度L_b>200 Å时, 衬底厚度的变化对薄膜中极化子的结合能和质量变化的影响不显著. 研究结果为GaAs薄膜电子和光电子器件的研究和应用提供参考. 关键词： 分数维方法 GaAs薄膜 极化子 低维异质结构     

Dimers on the kagome lattice II: Correlations and the Grassmannian approach

In this paper we continue our consideration of closed-packed dimers on the kagome lattice. Using the Pfaffian approach we evaluate the correlation between dimers on two lattice edges. It is found that the correlation is extremely short-ranged in the case of symmetric dimers weights. Explicit expressions for the nonvanishing correlations are obtained for two dimers in the interior of a large lattice. We also describe a Grassmannian functional integral approach, and use it to evaluate the dimer generating function and correlation functions.     

A scattering matrix approach to quantum pumping: beyond the small-AC-driving-amplitude limit

In the adiabatic and weak-modulation quantum pump, net electron flow is driven from one reservoir to another by absorbing or emitting an energy quantum hω from or to the reservoirs. This paper considers high-order dependence of the scattering matrix on the time. Non-sinusoidal behaviour of strong pumping is revealed. The relation between the pumped current and the ac driving amplitude varies from power of 2, 1 to 1/2 when stronger modulation is exerted. Open experimental observation can be interpreted by multi-energy-quantum-related processes.     

表面氧化层效应对测量临界点跃迁的影响：分数维空间方法

运用椭偏技术和分数维空间方法,对Si-SiO＿2模型考察了 表面氧化层的存在对从实验测得的光谱中确定Si临界点跃迁参数的影响. 计算结果表明，表 面氧化层效应使Si的介电谱发生畸变，由此得到的临界点跃迁参数较真值会有一个偏移：振 幅与维度值较小，寿命线宽较大，并且这种影响随氧化层厚度的增加而加强. 但禁带能受表面氧化层效应的影响却很小，可忽略不计. 关键词： 分数维空间方法 椭偏技术 表面氧化层效应 临界点跃迁     

Numerical resolution of the modified Langevin equation using a differential expression: Application to the Jiles magnetostriction law of approach

The Langevin equation is classically used to model the anhysteretic magnetization curve. A modified version of this equation has been introduced by Jiles to take into account the effects of magnetostriction on the anhysteretic magnetization behavior when a ferromagnetic material undergoes mechanical stresses. The numerical resolution of the modified Langevin equation is usually performed with a root-finding algorithm. In this paper, a differential form of the modified Langevin equation is proposed, allowing a faster numerical resolution.